A New Model of the Universe

(Entered in register of copyrights, Library of Congress, Washington, USA)

Anonymous

Conclusions of this work:

1. Explains how space and time can be finite without any boundary.

2. Explains how Time (before all events) in the universe can be finite without a beginning.

3. Explains how “God does not play dice”, that is, uncertainty may not be intrinsic to the universe.

Foreword

What you are going to read is something new and hereto unknown. What is scientific: that which is based on observations. To put this work in perspective, the approach here is to observe and understand the nature of observation itself, instead of looking for and interpreting a particular observation. These fundamentals of observation are important and their value in understanding universe will become self-evident.

An observer observes only the present and never the past.

It is impossible to observe past, only its remains or memory is observed in present. Evidence of past is etched in memory of the observer. Such memory can be part of observer’s mind or physical recordings. By observing such “recordings” – markings of past – observation of past happenings – the past is not being observed but only its evidence in the present. Light coming from distant stars has popularly been called as peering into past as light would have taken a long time to reach us. Or, visiting remains of a historical civilization also carries clues about its past. But the observer does not observe the past – only present. Observer himself remains in the present and observes present only and makes a personal judgment about his observation being a representation of the past. All observations happen only in present. One may conclude that past happened only by observing memory/evidence of past in present. This is not denial of past itself, but about mechanism of how we arrive at the confirmation of past. You can never re-observe what happened to you yesterday, you have a mental recording of yesterday in your mind or recording in whatever form – you can only observe the recorded “memory” of yesterday in present. This is not metaphysical; rather it is understanding the act of observation itself. Nor it is being insinuated that past did not happen, rather, all observations happen only in present – which include evidence of past.

We only observe PRESENT ARRANGEMENT of matter and energy around us.

Observing these words as they appear to you through whatever medium, and observing distant stars with powerful instruments, both are nothing but observing the universe around us. Then why would one observation be given so much more importance in understanding the universe? Universe is not just made of stars and galaxies, but also such mundane objects as furniture and personal effects. Stars, galaxies, kitchen table, the stray dust on it, moss on the wet floor of a shallow creek – all that is being observed by us now (we only observe NOW) is part of the universe. So as we observe all this, what are we observing – besides observing present, what else is common to all observations? It is that all observations are about observing arrangement of matter and energy in space. We only observe present ARRANGEMENT of matter and energy around us. This includes these words, the stars, your clock and memory itself. Memory – in whatever form, recorded mentally or physically – is just a subset of the arrangements that we observe and this memory is what we interpret as evidence of past. There is absolutely no other way of verifying that there actually was a past except by observing arrangements matter or energy representing past in present. We can never observe past directly, we only know present, and memory is part of the present arrangement of matter and energy.

Memory is ARRANGEMENT of energy and matter that is only observed in present (enabling us to deduce past)

Not just memory, everything in the universe is represented as arrangement of energy and matter. Memory is specially picked because it represents past and it gives observers a sense of flow of time, a verification of past, however, like everything else it is part of changing arrangement of matter and energy in the universe. Observer discriminates between which is objects are objects of observation and which objects are objects representing evidence of past. This is how all observations are made fundamentally. All conclusions drawn by any observer, right or wrong, are based on this fundamental mechanism that is used by all observers: Observer observers arrangement of matter and energy in the present but some part of it he classifies as memory as representing past. What arrangements are classified as memory (representation of past) are prerogative of the observer. The reason being anything can be classified as memory, because everything can be attributed to past. Which object represents memory and which is object under observer’s current observation, is entirely for the observer to “decide”. Another way of looking at it is, whole universe is memory – an arrangement of matter and energy representing its own past.

Memory arrangement and present arrangement work together in making an observation

Let’s say you want to measure speed of a car. You jot down its initial position and time while it is in motion, and then you again observe its final position and time. As you take your final measurement, you have the speed. But in this final observation, you observed memory in present (that is, jotted down initial position and time) and its present position and time. Therefore, in making this observation, you finally make only one observation in present, which involves memory arrangement and present arrangement. Therefore, we see that this observation, though it involved multiple points in time, it completed by looking at present arrangement only. All observations, including time dependent ones like this example, can be explained in this manner. The word ‘explained’ is actually a misnomer – this is how we ACTUALLY observe. This is how fundamentally an observation happens. All conclusions drawn by any observer are subservient to this foundation of observation mechanism. We as biological observers are “survival-trained” to discriminate between memory arrangements and others, but everything is just an arrangement in present, memory or otherwise. Take any observation of any complexity, at the point of making an observation it only involves looking at “recordings” of memory and present object(s) of observation. From there the observer works his way backwards, does his calculations yet, at every point in time he is only observing the present and present only – which includes of evidence of past. Just because we are “sure” that there was a yesterday, is not enough, it is important to know what makes us sure: this sense of “sureness” is our memory which is an arrangement in present. So we deduce all past out of our observation of present only, we don’t know past directly but only through observing our memory recordings of it in present. This is not a conjecture, all knowledge and observations for all observers happens through this mechanism. Therefore, these words are true and scientific.

So we see that even dynamic observations such as speed, acceleration and all others are actually derived from present arrangement only. This means, present arrangement of matter and energy in space, that is, present permutation of universe, completely determines everything that any observer observes in the universe. Any observation made by any observer, however complex, is by observing present arrangement only. Observers observe charge, magnetic and electric fields, velocities, time on clocks – or any other observables by observing present permutation only. This is not an alternative explanation of these observations, rather the actual observation mechanism – this is how these are actually observed by all observers.

All knowledge, all information, all observations, accumulated from past or made just now, all – everything that is observed one way or the other by any observer – all means all – no exceptions – are manifesting through the present permutation of the universe – our knowledge of genes, our theories of physics – a permutation is fountainhead of all, all else that we are so sure that it did exist or any derived conclusions that we arrive after years of labour, they come, but only out of witnessing present permutation. This present permutation of universe encompasses all observations of present and recordings of all past observations, because it is only present that can be witnessed. This makes all static and dynamic observations entirely dependent on the present permutation. Therefore, present permutation completely defines a state of universe.

The universe is a changing arrangement of matter and energy

This is all there is to the universe: changing arrangement of matter and energy. All manifestations of universe to all observers involve only the changing permutation of matter and energy in space. This is a very important conclusion. This holds true whether an observer is observing these static words or makes complex observations using powerful instruments. Observers observe distribution of matter and energy that is changing arrangement in space at all times. Change in arrangement of matter and energy is not just happening in distant stars and galaxies, it is happening at all levels and places including which are generally not considered of little “cosmic value” in terms of shedding new light on our understanding of the universe: flight of birds, our biological functions, falling leaves, ripples in a pond. But these are as much examples of energy and matter changing arrangement in space, as are galaxies and stars. Energy and matter is considered fundamentally the same and it exists in space.

Points do not exist

No observer can observe points, by definition they are unobservable – space of zero size. Therefore, points are metaphysical, their physical existence cannot be proven by any observer in the universe. For argument, one may assume there are minimal regions of space that are greater than zero, space of less than that minimal region does not exist. That is, space is quantized – larger volumes are made of smaller volumes, but there is a finite limit to which one can divide space into smaller parts and after that limit all observers will fail to observe smaller region. (Wavelength of the most energetic photon possible is the smallest observable length).

If universe is of finite size and remains finite

Imagine a universe that is continuously changing arrangement in finite space. It can be mathematically shown that such a universe will have only finite number of ways in which it can change its arrangement. That is, the universe will have only finite permutations to go before it will repeat one of its previous one. This conclusion is independent of principle of causality (cause and effect) and remains unaffected by principle of entropy.

Such limitation of finite spaced universe has some important implications. But why would universe be finite? I am keeping that out of foreword. If universe is finite, the matter and energy in it will have only finite unique permutations to arrange. After which, inevitably, one of previous ones, must get repeated. This takes us directly into the heart of what this work is about.

What finite universe means for time / clocks

Imagine a finite spaced universe with an observer in it with a set of clocks to measure time. For argument sake, assume the observer cannot die and his clocks do not break at any time. The clocks are ticking, any change within the clocks is also part of changing permutation of energy and matter in space of that universe. The matter and energy of the universe are changing arrangement, which are being witnessed by that observer. Only finite arrangements are possible for the universe’s contents – after which all the matter and energy will be in the same permutation as a previous one. When that happens, the observer will measure same time as before in all the clocks in the universe as they are also part of energy and matter in the universe. The observer won’t be able to tell this time apart from a previous time as all clocks in the universe will be showing the same time, also, arrangement of all contents in the universe will also be identical to a previous one. The observer shall conclude that the time that was, is back again. Unless observer thinks time behaves like ether which just keep flowing forward even if all else is identical. There is no basis to think like that, time is always pegged to a permutation, arrangements of hands of a clock, arrangements of planets, arrangements of stars, arrangements of atoms etc. When hands of a clock are the same there is always date calendar, when date calendar is same there is always something else to tell that time is not actually the same, our own memory and body clocks ensure that time is not the same. But when universal permutation is identical as in this example, to all observers all clocks are showing the same time respectively, including any biological body, clocks, date, calendar, stars, atoms and beyond. As seen above, a permutation completely defines all observations in the universe, so velocities and any other observable static and dynamic properties of its contents will become the same. The assumption that the observer does not die and the clocks do not break is dispensable and the conclusion will hold without it. They only make communication with reader easier. A point of interest here is that memory of the omnipotent observer is also part of the universe, and so is the observer himself. We know memory is also part of the permutation of the universe – as we have seen earlier. We shall revisit this indestructible observer.

How old is universe

Only finite permutations are possible in finite space. What is the magnitude of such a finite number? This is not a question that can be addressed. The numbers that we have encountered anywhere in our lifetime are meaningless when it comes to describing the present problem. The answer is just not feasible, even to answer a simple question for comparison: how many ways in which atoms in a drop of water can permutate? When one is supposed to answer it for the whole universe, it becomes just an unknown and finite, the only way to describe it. We can reach basic idea behind this model, that we observe changing permutation of matter and energy, using everyday mundane observations as well as observations made by most powerful instruments. It does not matter how it is being observed or what is being observed. But in terms of magnitude there is only finite time possible, even to conjecture on it quantitatively would be a fallacy. Its value to be a measure of a few billion years is not how one would look at it, a conjecture, say one followed with as many zeros as there are atoms in the observable universe is time/age in years of universe - may be an underestimate. But to measure time, we need a unit, and to measure age of universe we need a unit that will remain intact throughout all time. If no such unit exists, then theoretically it is meaningless even to conjecture on maximum possible time in universe. To understand it better, let’s go back to the previous example, in which an observer is in finite space with his clocks. Since clocks are part of the universe, they may breakdown as part of changing permutations. When the clocks are not there, the unit of time with which time was being measured becomes meaningless. Therefore this observer will not be able to tell us the time it took for the permutations to finish. (Nor it is necessary for all mathematically possible permutations to become reality. All that is being stated is: after finite permutations it will be inevitable for permutations to start repeating.) So in the real universe, the unit of year will become meaningless once solar system disassembles. Definition of second will become meaningless if the element used in defining second ceases to exist in that form. Overlapping of interchangeable units before a unit of time breaks down is a pre-condition if a superior indestructible observer would like to make a measurement on maximum possible time of the universe. That is, such an observer is observing and measuring passage of time, before one unit of time ceases to exists, it is converted into another unit of time by this observer as both units existed simultaneously, so that if one disappears, the other unit is available to carry on the measurement – until all permutations are done. At that time, all the measurements are converted into a base unit of measure of time and we have age of universe in say – years.

But there is a catch.

What it means for indestructible observer observing everything

Assuming a superior indestructible observer is observing everything throughout all times. This observer is part of the universe and made of matter and energy of the universe. He is keeping track of everything that is happening in the universe, every speck or atom and smaller particles of any scale – but still he himself is part of matter and energy that makes this universe. For the sake of simplicity, let us assume we have a unit of time handy which remains valid throughout all time. And time starts now. Let the count of time begin now, to begin with it is zero. When the same permutation (as now) will happen again, must not then indestructible observer observing everything know how much is the count? Answer is, no. Keeping count is part of this observer’s memory – and memory is part of permutation. Therefore, when the same permutation (as now) will happen again, the count should also be the same. That means zero. By implication, when the count ends, instead of having an answer, he is starting counting of time all over again! The only way to explain this is that this most ideal observer, somewhere along the way must forget what he was doing, lose his count and start again. He will never have a final answer; this information must be lost in order to arrive at the permutation of ‘now’ because ‘now’ permutation exists only with a zero count in this observer’s memory. If he gives the final answer to be a non-zero one, he has stopped his counting at the wrong permutation, it definitely is not the same one as at zero, for even if everything else is the same, his own memory that is part of the universe’s permutation is not the same. He must comeback to zero to conclude, yet that conclusion is loss of count itself. It is somewhat like when we are counting something and we lose track and then we start counting again. In this model this is the fate of the best-equipped observer while trying to measure full length of time in universe from within the universe.

This explains futility of going into quantitative details of time in universe. It is finite for all observers and that is the maximum they can conclude.

General remarks about this model vis-à-vis contemporary model

This model is not a creation or beginning of time model; rather, it is about universe as having finite time and space, and it explains how time can be finite, if space is finite. According to it, universe exists at all times, it also remains finite time old at all times. Just because universe never got created does not mean that it is infinite time old. In isolation the previous sentence sounds completely wrong, but in view of all that is mentioned in the previous pages, there should be some understanding for this view by now. The work does bring about new understanding of time – as arrangement of things. The reasoning is tied to observations but not to any specific observations, rather to all observations because arguments are based on fundamental commonalities between all observations – their fundamental nature. The crux of the model, that is, finite space must lead to finite time, is something completely new and hereto unknown. Given the scale/magnitude of time discussed above, evidence of big bang may be a local event happened in the very near past of about 15 billion years, and to turn it into start of time itself may be wrong. If convincing evidence of objects which are older than big bang is discovered, that could be an indication that that big bang event is not start of universal timer. However, this work is not about finding faults with the big bang theory, but it is about explaining a new model, which has finite time as well as does not have a beginning.

The point being made in this work

This work introduces of a vastly different model; this model is not based on some observations, rather fundamental nature of observation itself, which is combination of observer, observed and memory of observer – which forms a part of the universe permutation in which the observation is being made. A permutation completely defines an observation: All observations are made in present only, and that includes those that involve multiple readings across time, as all past readings are nothing but present memory – hence part of present observation. Given finite space and quantized space, mathematically only finite permutations are possible, hence finite time is possible. Same permutation means same time because all clocks and all other observations will also be the same if the permutation is same. As a permutation completely defines all aspects of an observation, therefore all observers will be making the same observations when permutations are identical – hence time will be the same. Therefore, time of the universe can be finite without a beginning.

I am not sure if this has been expressed elegantly enough, but it is not about flair, it is not about many things, if not all, not even the way in which words have been juxtaposed, it is about resolving a paradox that makes big bang awkward and all its alternatives unacceptable: Infinite time before an event is a statement of impossibility for that event to ever happen. If it is happening, it could have happened only after finite time. Infinite time before now makes everything that we observe now an impossibility – yet it is happening. So must we have a beginning of time? That is what makes big bang appealing, for it gives us a beginning for the universe, finite time before now. But the beginning itself, how can that happen? As long as there is a beginning of time, there will be questions about how it can begin, and as long as there is infinite time in past, present should not be. This paradox remains.

But there is a way to keep time finite before now without a beginning. This is that model.

CHAPTER 1

Imagine other forms of intelligence, perhaps of microscopic dimensions and they too have set their minds on investigating the universe around them. What they will conclude about the universe? Their view of universe may be a lot different from ours, unless they have the similar information and data at their disposal. We have access to many different types of instruments. We know there are galaxies, there are atoms, we may not see them directly but we have tools to help deduce them. Those other forms of intelligence may have their own tools, their own observations and their own conclusions. If they cannot see what we see then their understanding of the universe may very well end up to be very different from ours. They are not to blame, nor we, we are interpreting nature of universe by looking at very specific observations: galaxies, moving away – that’s how universe is for us. Other forms of intelligence may not be able to see those galaxies, but their own very specific observations that they attach universal importance to, hence different conclusions. A better model is one that can be derived by all observers anywhere in the universe, regardless of observers’ technological limitations. Understanding fundamental model of universe is not tied to a particular set of observations, but how fundamentally any observer anywhere in the universe makes observations, regardless of what is being observed.

As discussed, we only observe changing permutation of matter and energy in present. This chapter broadly mentions those specific observations, which tie us to our contemporary understanding of the universe.

Our modern view of the universe started taking shape in 1924 when it was discovered that ours is not the only galaxy of stars. There are many other galaxies similar to our Milky Way. In order to prove this point, it had to be shown that some clusters of stars are so far away that they form an independent separate entity of their own as a different galaxy. If one could determine distances to these galaxies to demonstrate that these distances are much larger than that of nearby stars that would show that these clusters are not part of Milky Way but they are independent clusters of stars like Milky Way.

From a moving train we see that trees, which are nearer to the track, appear to move faster than the distant ones. In the same manner as the earth goes round the sun the nearer stars appear to shift more than the distant ones. Using this simple phenomenon we can determine distances of nearby stars. Unlike the nearby stars, some clusters of stars do not show any perceptible change in their positions throughout year as earth goes around the sun. Relative stationary positions of these clusters in the sky indicate that these clusters are so much far away that any shift in their positions is imperceptibly small. This forced use of indirect methods to measure the distances to those clusters of stars.

The apparent brightness of a star depends on two factors: its distance from us and the rate at which it is emitting light, that is, its luminosity. So if we know apparent brightness of a star and its luminosity, we can work out its distance from us, or if we know distance and apparent brightness then we can work out its luminosity. Basically, we must know any two quantities to find the third one. For nearby stars we can easily calculate their apparent brightness and distances. Once two of the three quantities for nearby stars are known the third quantity (i.e. luminosity) can be found easily. In this way one can determine all the three quantities for nearby stars. However, for the nearby stars it is observed that certain types of stars always have the same luminosity. If one can search for those certain type of stars in those stationary clusters and assign them the same value of luminosity two quantities would be known (namely, apparent brightness and luminosity) about the stars which remained stationary in sky throughout year. Then calculating distances to those stars was not much of a problem. By calculating distances for a number of stars in the same cluster and getting more or less the same distance each time not only corroborated the idea of galaxies but also vindicated the technique followed in the process.

Discovery of galaxies was a major discovery of the times. It highlighted the role which spectra of stars can play in gathering more knowledge about the cosmos. This generated considerable interest among astronomers to have a better understanding of spectra of different stars. In the following years lots of information gathering regarding the spectra of various stars was done which was followed by some careful analysis. It was found that certain very specific colours were missing from spectra of stars and also that the missing colours may vary from star to star. These missing colours in the spectra of different stars gave important information about the atmosphere of the stars. It was known that each chemical element absorbs a characteristic set of very specific colours. By correlating this knowledge about different elements to the missing colours from a star’s spectrum one can find the elements present in the star’s atmosphere. An observation of immense importance was made in the late 1920s. While matching spectra of stars of other galaxies with the stars of the Milky Way, astronomers found that there were same characteristic sets of colours missing for both sets of stars, but for the stars of other galaxy, all the missing colours were shifted by the same relative amount towards the red end of the spectrum. An acceptable explanation for these observations could only be made possible when astronomers tried to analyze it in the light of a well known effect exhibited by sound waves.

Imagine a bell, stationary with respect to an observer, emitting constant number of beats with time. Since distance between the observer and the bell remains constant, the observer will hear the same number of beats in unit interval of time as emitted by the bell. Suppose the bell starts moving towards the observer at a speed less than the speed of sound. Now as the bell emits any two consecutive beats it travels some distance towards the observer. This means that the latter beat travels less distance than the former one to reach the observer. This results in reduction in time lapse between the sounding of the two beats for the observer. Interval between the sounding of the two consecutive beats gets reduced, or in other words the observer will hear more number of beats in unit time in comparison to when the bell was stationary. Correspondingly, if the bell starts moving away from the observer, the observer will hear less number of beats in unit time in comparison to when the bell was stationary. In this way frequency of sound waves may get increased or decreased depending upon whether the observer and the source of sound are coming close or moving apart. This phenomenon which affects all kinds of wave motion was first noticed in sound waves. Light waves too exhibit this phenomenon.

Through direct observation astronomers were quite sure that stars of the Milky Way are relatively stationary. So the spectra which the astronomers were receiving from nearby stars were the same as emitted by the stars. That is, the missing colours were in the right place for the nearby stars, whereas in the spectra of stars of any other galaxy all the missing colours were shifted by the same relative amount towards the red end (that is, towards the lower frequency region) of the spectrum. This means that from other galaxies they were getting light of lower frequency than it ought to be. The light waves coming to the earth from millions of light years conveyed something the least expected: the galaxies are moving away from us, that is, the universe is not static!

Before this discovery was made, astronomers used to believe that the universe is static and remains more or less unchanged with time. Although they were having hard time in explaining this, they could not think beyond this as they had no reason to disbelieve this, for skies had remained unchanged for centuries. But the idea of a static universe always remained an enigma after discovery of the law of gravitation in 1687. According to this law all bodies of the universe attract each other, so if the universe is static then all galaxies must have started coming closer and had eventually collapsed on themselves. If the idea of a static universe is really true, then the universe ought not exist in the way it exists, it should have collapsed on itself. Our consciousness of existence and our quest for solution of these oldest riddles are evidence that the universe is not the way they had assumed it to be. We must straightaway reject those models of the universe which prohibit us from existing.

A careful study of red-shifts of various galaxies was done and further findings were still more spectacular. It was observed that the extent of red-shift is not same for all galaxies. That is, red-shift is different for different galaxies. On further investigation it was discovered that the extent of red-shift for a galaxy is proportional to its distance form us. The extent of red-shift is nothing but a measure of speed with which a galaxy is moving away from us. So in a way this pointed out that the speed with which a galaxy is moving away is proportional to its distance from us. That is, distant galaxies are moving away faster from us. The conclusions derived from this finding were dramatic. Now astronomers knew that the universe is not static but it is expanding like a balloon being inflated. The galaxies are like spots on the balloon, which move apart as the balloon is inflated - farther the spots, faster they move apart.

As distance between galaxies is increasing the universe is growing in size. In other words, galaxies were closer and the universe was smaller in past. Thus, there must had been such a time when distance between neighboring galaxies was zero. That is, once upon a time universe was infinitesimally small. Based on these ideas and observations a theory called the big bang theory was postulated in the 1920s. Accordingly to this theory, about 10-15 billion years ago the universe started off as a submicroscopic, unimaginably dense knot of energy that flew outward in all directions. Over the time, expanding and cooling, became galaxies, stars, planets and evolution of life happened on earth.

Though it was now known to the world that the universe is not static, some thinkers still believed that even though the universe is not static, it still remains more or less unchanged with time and had existed for always without there being a beginning in the form of big bang. In 1948 a theory, called the steady state theory, was proposed. Unlike the big bang theory, in this an infinite model of the universe was proposed. It was based on a very simple assumption that the universe always existed and remains more or less unchanged with space as well as with time. Accepting that galaxies are moving away, it was proposed in the theory that as galaxies are moving apart new matter or energy is continually getting created in space to fill the gaps between them. In this way new galaxies are continuously getting created so as to keep the universe unchanged with space as well as with time. So the universe should always look similar in all directions from anywhere in space.

A survey of radio sources from other galaxies was conducted by astronomers during the 1950s and 1960s. They showed that there is no way the universe is as symmetrical as predicted by the theory. That the universe is not following any steady state was an evidence convincing enough to stop pursuing the theory any further. It was abandoned.

In the same year "hot big bang model" was introduced. In this model of the cosmos it was assumed that at the time of the big bang the universe had zero size--that is, the universe was infinitely dense--and infinitely hot. After the big bang, as the universe expanded, any matter or radiation in it got cooler. Since temperature is a measure of average energy (or speed) of particles, the cooling of the universe had effect on matter. At times when the universe was very dense (that is, at very high temperature) particles were moving so fast that no force of attraction was strong enough to hold them close together. But as the universe expanded (that is, at comparatively lower temperatures) particles slowed down and started attracting each other to join to form regions that were slightly denser than average. Those slightly denser regions have since evolved into galaxies which are moving away as the universe is still expanding. Along with the theory it was also argued that the radiation from the early hot universe should be around even now. Since the universe is expanding, we are moving away from the point of the big bang, therefore the radiation should be red-shifted by so great an amount that it should manifest to us as microwave radiation.

In 1961 accidentally a radiation was discovered. The detector was picking more noise than it was expected to. Initially the source of the radiation, which was manifesting itself with so much noise, remained a mystery. After many recheckings of equipment for any defects or malfunctioning and changing the detector’s position, it was concluded that radiation was not coming from any particular direction or source. The level and quality of noise remained unchanged with day, night and season. Since it remained unaffected by detector’s location on the earth as well as by the earth’s motion around the sun, the only way out was to conclude that the radiation was coming with equal intensity from all directions outside the Milky Way. It was this radiation whose presence was predicted by the “hot big bang model” in 1948. In this way cosmic microwave background, the original radiation from the big bang was laid bare before the world.

The idea of big bang remains successful, that the universe had a beginning as a “point”, infinitely dense knot of energy that flew outward in all directions. The universe was so intensely dense that all the theories, which we formulated 10-15 billion years after the big bang, would breakdown at the time of the big bang. Hence, there is no way we can determine anything about before the big bang. This means that even if there were events before the big bang, we cannot use the post-big bang scenario to determine anything about the pre-big bang times. Therefore, scientists say that events before the big bang are of no consequence and should not be considered as part of a scientific model of the universe. We should therefore cut those unknowable events out of the model and say that time had a beginning with the big bang.

Having rejected the steady state theory, the infinite model of the universe, the universe is finite in extent and it is expanding as the galaxies are moving apart. It is the fate of the universe which remains unknown. For how long will this expansion of the universe go on? Will it go on forever? If not, then what are the other alternatives? Will galaxies stop going any farther after some finite time or perhaps even start moving back to the same point from which they came into being in the first place with the big bang? What are the forces that govern the fate of the universe?

Before going for the possible answers to the above questions it is important to know something about gravitation. It states that all bodies of the universe attract each other. (The force of attraction between any two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.) Earth’s gravity constantly keeps pulling us to keep us near its surface. It is the same force, the gravity, which brings a thrown stone back to the ground.

The general theory of relativity states space is not flat, but it is curved by the distribution of mass and energy in the universe.

A straight line is the shortest distance between any two points. Light, which travels fastest in the universe, moves in straight lines. If space is curved, that implies light should not appear to travel in straight lines in space. The theory of general relativity predicts that a great mass would curve space so much that it would result in the bending of light which can be detected.

If a massive mass curves space which results in bending of light coming from the other side, then the position of the source of the light should appear shifted every time that mass comes between the observer and the light source. Since the apparent shift in the position of the source happens only when the massive body comes in between, one can be sure that it’s the gravitational field of the intervening body which is curving the space and consequently bending light. This phenomenon of bending of the light near massive bodies has since been confirmed many times and the general theory of relativity is considered as one of the most revolutionary theories.

We know that the universe is finite in extent and galaxies are moving away from the point of the big bang. At the time of the big bang an explosion took place whose causes cannot be known, but its effects have been detected. It is only the effects we know—by which we deduce the big bang - and not the big bang itself. In that explosion, so much energy was imparted to what we now call the galaxies that they are still moving away, even billions years after the big bang. The law of gravitation says that they are attracting each other, but the energy imparted to them is so great that they cannot but keep on moving further apart. It’s like a stone thrown skywards. The earth is attracting it all the time while it is going up, away from the earth due to the energy given it to by the thrower. But ultimately the gravity is compelling enough to make the stone change its course of motion and fall back to the earth. Had it been a space rocket, if all goes well with its machinery, it wouldn’t have fallen back but gone to the outer space. Similarly, the galaxies are attracting each other but are compelled by the energy imparted to them at the time of the big bang to move away. It’s a tug-of-war between the force of gravity and the energy with the unknown causes. If the gravitation prevails, the galaxies will fall back to the point of the big bang, otherwise they will get away to the oblivion, forever moving away to “infinity”.

We know that the force of gravitation is proportional to mass. So if the expansion of the universe should come to a halt and the consequent fall of the universe on itself, the universe should have sufficient mass in it to make that happen. This mass of the universe should be so much that for anything to escape from the universe, it has to attain a speed which is greater than that of the speed of light . As nothing can travel faster than light, then nothing could escape (not even light) from the universe if it has got that much mass. Instead, whole of the universe will fall back on itself like the stone that failed to escape from the earth. This ‘falling back’ of the universe can also be called the contraction of the universe (opposite of expansion of the universe) which would finally lead to the big crunch (opposite of the big bang).

Big Crunch

Big Bang

Like at the time of the big bang, at big crunch too all our theories would break down as then the universe would become as dense and as hot as it was at the time of the big bang. So we cannot predict anything about the post big crunch times. Thus, we can very well label it as the end of time, just as the big bang is the beginning of time. Another remarkable feature of this model (the universe having enough mass to collapse on itself) is that in it at no time the universe becomes infinite in space. And this finite space does not have any boundary in space because in this model the gravitational forces are so strong that space of the universe gets completely curved on itself. In such a curved universe if a body keeps moving in one definite direction it would come back to the same point from where it started . In this model the curved universe would be finite without any boundary like the surface of the earth, which has no boundary, and yet it is finite – but in three dimensions instead of two. Thus, if this is the real case then spatially the universe is finite with a definite beginning and end of time.

If the above case is not the real one, that is, the mass of the universe falls short of the critical value of the mass required for the big crunch, then there is nothing that we know that can stop the galaxies from moving further apart forever. Then there won’t be any big crunch, no end of time.

Separation of Photons

TIME

Big Bang

Ultimately, the question concerning the fate of the universe comes down to a simple issue: will the galaxies stop moving away and then finally reverse the expansion of the universe, or not.

These are the some of the main observations on which contemporary understanding of universe is based. They are complicated, demand sophistication and ingenuity. But they are all observed by observing permutations of energy and matter in finite space. Big bang as beginning of time is an idea and not an observation. These observations and theories, I have no basis to question – except idea of big bang is not the beginning of time.

CHAPTER 2

The innate property of our mind to sense, to feel, the consciousness--of subtle passing of time--of being , is what makes us living. Ever since we learnt to think this elusive feeling of passing away of time has baffled us. How is that it always churns out future and never past? Direct observation of past is an impossibility. As realists we are supposed to stare at what is, and not ponder over what cannot be. We only know present that is changing all the time. Time is a concept arising from change experienced and observed. Here change is the key word; though it is not synonymous with time, time derives its existence from changing arrangements of matter and energy occurring everywhere. Imagine a universe that is not changing--everything, each single entity constituting that universe is perfectly still. Won’t time be meaningless there? To show that it does become meaningless, let’s assume it doesn’t.

For time to be meaningful there should be distinctly different past, present and future. So the unchanging universe must have past, present and future for time to be meaningful in it. This means that the now unchanging universe had been changing, but due to the effect of some laws governing that universe it has stopped changing, and also that after some time the universe must start changing again without any extra-universal (whatever that means) intervention. Only then there can be distinctly different past, present and future for time to be meaningful, as we have assumed.

All we know is that it has not been changing for some duration. If changing universe is not changing for some duration, this means for this duration all clocks have stopped moving – therefore if an observer were to measure this duration he will always measure zero time, as all his clocks would not have registered any change in time. Therefore this duration is always of zero duration. Actually this observer could not even conduct such an experiment because his body clock too would have stopped, no observation is possible in an unchanging universe. This so called temporary stagnation amounts to nothing but zero duration, because no clock in such a universe would have measured any time interval. Hence a universe’s temporarily becoming unchanging is meaningless as it is undetectable to all observers – hence it is metaphysical. This means if it is unchanging it must be permanently unchanging – and no observers will know that such a universe exists. This makes even a permanently unchanging universe, is a metaphysical idea. (The universe that is now unchanging had never been changing and nor it could ever start changing by itself. Thus, there is no distinction between its present, past and future - for all three being the same, as the universe is not changing at all. Therefore time is meaningless for an unchanging universe.) Having ruled out possibility of unchanging universe, in the realm of physical world we are left with a changing universe only. Not just this, a universe that is now changing, was always changing for all times. If it were not the case then it could not have started changing on its own.

In the cosmos change is an omnipresent phenomenon. Our stint with life comes to us through this phenomenon going around and within us. Although time to observe and experience is limited, the question, ‘How long in this universe the show of change will go on, and also for how long it had been going on?’ remains. The answer to this is in the previous paragraph. Any universe that is unchanging shall be permanently like that. This means that a changing universe was never stagnant because if it was like that it will be the violation of the conclusion stated in the previous sentence. The real point being made is that a changing universe had always been changing. (If universe had always been changing, we can extrapolate this changing nature to future as well. If a changing universe stops changing – time becomes meaningless for it. Just like permanently unchanging universe cannot start changing, a changing universe cannot become permanently unchanging.)

Regardless of any arguments presented above, in the final analysis, change in universe is an empirical phenomenon universally observed by all observers. Therefore, its acceptability as a universal phenomenon is beyond doubt. Change is happening in the universe independent of time and scale. All observations are only observations about changing universe. All laws of nature, known or unknown, correct or incorrect, partial or complete are based on the fact that universe is changing. A law of nature that predicts that universe was or will become unchanging is only predicting its own downfall because every law becomes known and observable by changing universe. Such a law itself is inapplicable when it approaches a time when it predicts cessation of change in the universe. Change must be part of a model of the universe. Any model of universe, which fails to incorporate change, is simply not complete. Though it is not quantitatively describable like gravitation (gravity too manifests itself through change), nevertheless, it is a universally observed phenomenon accepted as a universal fact.

At any time in the universe one can be sure that the universe shall be changing. This is independent of all conditions prevailing in the universe at any time. Time cannot stop or start: the change in arrangement of matter and energy must keep on happening at all times in the universe.

Ever-changing universe leads to the conclusion that time extends to infinity in both the directions – past as well as future. At this stage one sees no way to avoid this conclusion. As I write I find my thoughts have irrevocably locked horns with the big bang theory. Why time had a beginning 10-15 billion years ago with a primeval explosion called the big bang, while the universe should be changing always in past? Or, if universe was permanently unchanging, how it could begin changing? Why do we call it the beginning of time? What sense does the concept of ever-changing universe make in making us understand the universe better? Or does it not, as it may seem, intricate it even further? A valid objection to this concept of ever-changing universe is that if the universe had always been changing then for every event to occur there will be infinite amount of time before it, and since infinity is something quite unachievable why will any event ever really happen?

For however long duration the universe ‘waits’ for an event, infinity still remains infinity--it never arrives. Infinite time is impossible to achieve. If an event has to happen infinite from now in the future, we can conclude that that event will never happen. There cannot be infinite time before any event if it has to happen. But the moment we know that the universe should be ever-changing in past we are compelled to conclude that time extends to infinity in past – which is impossible because present events are happening. There being infinite time before any event means that the event’s turn should never come and therefore it should never happen. So there has to be only some finite time before all events because they are happening. But the universe should be ever-changing also, yet ever-changing means present should not be.

So here we have two conflicting statements. As an attempt to solve this paradox, beginning of time is in place for the contemporary model of the universe (though only one of the statements is addressed in doing so). According to it the universe started changing only some finite time back in past and before that it wasn’t changing at all. It was just a singularity--a point having all the energy of the cosmos. It wasn’t changing at all, so time was meaningless. It became meaningful only some billions years ago when the big bang must have occurred. In this way before all events of the cosmos there is only some finite time, and hence events of today have every right to happen. But how is it that an unchanging universe starts changing by itself? How come that time suddenly becomes? It wasn’t there at all, and then suddenly it is! Isn’t it like admitting to the occurrence of divine intervention? The question marks remain. Big bang helps, it gives us the right to be, as there has to be only some finite time before us for us to exist. If we squarely face these question marks with ever-changing nature of the universe, we know – yes it is impossible, the universe had to be changing, ever-changing rather. But if the universe shall always be changing then we automatically tumble to the wrong conclusion that time stretches to infinity in past.

We come to the conclusion that there are two ideas and both of them must to be correct. One is that of ever-changing universe and the other is that there shouldn’t be infinite time before any event. But how can both of them be correct? One defeats the other: ever-changing universe means that there is infinite time before all events and finite time before all events means that universe was not ever-changing. And yet both of them should be correct! This is impossible--if you’re wondering this, then you’re getting the point! The pointers of thought are steering us to both these ideas even while they could not stand each other. Surely some link is missing somewhere. Let both the ideas remain as they are, even though they’re conflicting, and try to understand their repercussions on understanding how the galaxies happen to be moving apart.

Knowing that the universe is expanding, all possible histories that the universe could have had are:

1. Size of the universe was zero some finite time back in the past. Then the universe was infinitely dense with all the energy concentrated over a single point.

2. In the past the universe was smaller and still more smaller but was never as small as a point. That is, the universe has always been expanding, and as we look any time back in past we see a universe which can be very small but never as small as a point. (Imagine a sphere which contracts to half it’s size as each second elapses. In finite time it’s size will never become zero. Now reverse the direction of time, that is, instead of contraction make it expansion. Thus the sphere never had zero size and shall always be expanding.)

3. The universe was smaller and smaller till it was of some fixed finite non- zero space in finite time in past and the universe was never smaller than that finite space.

4. (Like the second history in this history also the universe was always expanding.) In the past the universe was smaller and smaller but was never smaller than some finite space. (Imagine a sphere which contracts. But as it contracts the rate of its contraction decreases in such a way that it tends to reach some finite size--without ever reaching it. Now reverse the direction of time. Thus the sphere had never been smaller than the finite size and shall always be expanding.)

5. In the past the universe was smaller and smaller till it was at its nadir, and before the nadir the universe was contracting. That is, far back in the past the universe was contracting till it reached the nadir, and since then it has been expanding.

Out of these five histories only one is the true qualitative description of the archaic universe. Following is the analysis of each one of the above histories based on the already specified criteria (that is, infinity in time never arrives and the universe should always be changing.)

1. Size of the universe was zero some finite time back in the past. Then the universe was infinitely dense with all the energy concentrated over a single point.

This history is not accepted as it professes beginning of time and contradicts the idea of ever-changing universe.

If in our minds we follow a journey backward in time, there won’t be any end to it. Small, smaller and still more smaller it’ll keep on becoming and it will continue like this endlessly irrespective of how much time back in past one wonders. Thus about whatever time one may think of, there would still be infinite chunk of time before it. So before all events, the universe had to go through infinite time. That is, any event, however archaic, if it has happened, it happened only after an infinite wait. Infinity, the concept which by its very definition means something limitless and endless, how could it ever have come to an end? It just cannot. The answer to the question brings home the conclusion. It is not the history we are looking for.

3. The universe was smaller and smaller till it was of some fixed finite non- zero space in finite time in past, and the universe was never smaller than that finite space.

It is quite possible since, unlike the first history, in this case though the universe was small but it never acquired zero size. According to this history, for all times before some finite time in past the universe maintained some fixed finite non-zero size.

Like a time activated explosive device containing a clock that keeps ticking before the bomb explodes, the universe was ever-changing in that finite space until some finite time back when something happened that resulted in the expansion and the consequent unfolding of the universe to it present form. That universe could be ever-changing within finite space makes this history all the more acceptable.

But it is not the history, there is a catch in it. It will be dealt later in this book. It is purely on the basis that it will be justified later, I presume that this history is impossible.

the finite size and shall always be expanding.)

According to this history the universe had always been expanding. This always expanding universe means that there would be infinite time before all events, like in the second history.

That’s impossible as there cannot be infinite time before an event. This history is not acceptable.

A question that arises is where all that converging (contracting) energy of the universe was coming from? A classical answer to this could be that all the energy started converging to form the nadir from infinite distance and also that present expansion is nothing but a voyage back to infinity. Thus, all energy reached the nadir after travelling infinite distance. This means that it must have taken infinite time before the nadir could have been achieved. That is simply impossible for there is no way the nadir could ever have been achieved if there was infinite time before it. At whatever finite speed energy of the universe converges there would always be infinite distance left for it to travel. So the nadir should never have occurred if energy of the universe was really approaching from infinity.

The only other way left is that converging energy of the universe was coming from some finite distance. That is, the pre-nadir contraction of the universe started some finite time back within finite bounds of the universe.

But how did energy of the universe manage to reach there? Surely it could not have come from beyond finite distance because then it would mean that the contracting universe was coming from infinite distance. We already know that it is impossible. The mystery that still lingers is that if not from infinity then where from that contracting universe came into being?

A possible way of explaining this is that previous to the beginning of the contraction, the universe was always of some fixed finite space (for it cannot be infinite) and it was ever-changing within that finite space. As the universe was changing it stumbled on such a happening from within which produced such an effect that the universe started contracting. And hence the nadir and present day expansion of the universe.

On closer study of this explanation one cannot fail to notice the similarity between this and the third history. In the third history also the universe was supposed to be ever-changing within some fixed finite space and then some finite time back something happened and the universe started expanding. In both the cases the universe was always of fixed finite space until: in one case the universe (is supposed to have) started expanding whereas in the other it (supposedly) started contracting. It is this similarity (in Italic) between this explanation and the third history that makes them both unacceptable – as will be seen later.

The contracting universe could not be coming from beyond some finite distance. Nor it was always of some fixed finite space. There is just one alternative left unexplored. That is, the contracting universe came into being from within and not from without. That the universe was actually expanding before it started contracting. All other possibilities have already been ruled out. Thus the now expanding universe was contracting, and before that it was expanding! That expansion of the universe can be investigated in the same manner as we did for the present expansion. Thus before that expansion it should be contracting, and before that contraction it had been again expanding! In this manner we can keep going back endlessly. Thus, after ruling out other possibilities we come to the conclusion that present expansion of the universe can be explained only if we accept that the universe had been expanding and contracting ever since.

Evidence of objects older than big bang or evidence that universe can contract in the future will support the fifth history. Any observer anywhere in universe, once he concludes finite spaced universe, it does not matter if that observer observes galaxies or that observer itself is spread across galaxies and sees universe far beyond what we know, nor if the observer is so acute that it is incapable of observing more than one micron across, they all will reach the same model of the universe – without need to know cause and effect mechanics of any theory of Physics.

According to general theory of relativity space is not flat, but it is curved by the distribution of matter and energy in the universe. Based on this theory in the first chapter expansion and consequent contraction of the universe was explained as that in such a model at no time the universe becomes infinite in space, and this finite space does not have any boundary because gravity curves space of the universe completely on itself.

The only difference between that model, which was discussed in the first chapter, and the fifth history is that whereas in that model the universe expands and contracts only once, in the fifth history it is an ever-going process. There is no reason as to--if the universe is considered finite and unbounded in that model, why it should not be considered finite and unbounded for the fifth history. For the fifth history also the universe is like the surface of the earth--unbounded and finite--but in three spatial dimensions.

Imagine a hundred people going away in different directions from a single place on the earth. In the beginning all of them will be moving away from each other. Supposing that none of them lose their direction and they manage to surpass all obstacles, after some time they will actually find themselves coming closer to each other. It’s the same with galaxies in the finite unbounded universe in the fifth history – as galaxies keep moving away, after some finite time, they actually start coming closer to each other because gravity has curved the universe so much that it has become circular – that is, spatially finite without any boundary.

In the fifth history the universe is concluded to be finite without any boundary. But many questions are left unanswered. The conflicting criteria with which the analysis was done –that change is the ever-present property of the universe and that there cannot be infinite time before any event--is yet to be vindicated. How does this criteria hold good for the finite boundary-less universe just as it does not hold good for all other histories? What’s wrong with the third history? How time before all events is finite in the finite boundary-less universe. It’s like having reached the conclusion by selectively avoiding the real issues! Why I cannot straightaway answer all that here and now?

All these questions are answered in the following chapters.

CHAPTER 3

All time measured by any observer in the universe pertains to arrangements. All clocks reveal time by showing an arrangement, hands of mechanical clock, digital watches, quantity of water flowed in a water clock or sunrise as arrangement of Earth and Sun. All observations are about observing arrangements of matter and energy only, that includes speed, weight, force, a wave, printed words and memory. All observations are derived out of permutations only. Any observation made by any observer in the universe can be traced to objects under observation and all past measurements pertaining to those objects are nothing but present memory – that too is part of the present permutation. Objects being observed and memory being observed, both are part of the existing present permutation. It is permutation that remains common to all observations, no matter where they are made in the universe. Past is never observed; only its memory or evidence is observed which is part of present. Only present is observable which embodies in it evidence of past. Therefore, all observations are made by looking at the present permutation only. (What is “present”? Observers observe objects only because they are present. This premise is foundation all scientific understanding, interpretation of what is present and how it came about comes after observer accepts that the observed objects are present.) All observations, including those that are apparently made across time, are made in present only as all past measurements are rendered to memory, which is part of present permutation. This is actually how observations are made everywhere in the universe by all observers therefore all knowledge about the universe for all observers is secondary to this principle.

It is not implied here that there was no past; rather we know that there was a past by only looking at its evidence in present. As organic observers we are creatures of habit, we observe past without realizing that it is not past itself but its evidence rendered to memory that is being observed in present. Direct observation of past is impossible. When we look at light coming from a distant galaxy are we looking at past? Popularly it has been referred as such by scientists, but it is untrue – we only witness light that is in present. Subject to observers’ interpretation, that light represents something in the past, just as printed words represent something of the past, but the observer is witnessing both in present only. Observer only observes present and concludes out of present that past was.

It is assumed that space is quantized, that is, observable space is collection of minimal finite non-zero spaces, and smaller spaces than that do not exist. If space is quantized, permutations are finite in finite space. If there are n positions possible for k particles, it can be shown that these k particles can arrange in those n positions in only finite number of ways as long as n and k are finite irrespective of their magnitude.

Even if space is not quantized, that is, it is continuous the conclusion of finite permutations remains valid. If there is no minimum limit to space except zero, after finite permutations in finite space, new permutations will resemble previous permutations with more than any given degree of accuracy so that no observer will be able to tell them apart. Eventually, deviation between these permutations will become indistinguishable for all observers. Which means that all observers in the universe will end up making identical observations (as compared to when the similar permutation happened earlier) because all observers will be observing objects (and memory) in positions that will be indistinguishable.

We can place an observer made of matter and energy anywhere in the universe to conduct a thought experiment. This observer has limitations up to which he can measure positions of objects. These limitations are finite, as long as he measures positions and records them, and we can show that there comes another time when this observer, again bound by the same limitations, again makes the same observation about objects in his surroundings. We have to conclude that he is observing the same permutation as far as he is concerned. When all observers in the universe are unable to observe any “difference”, the permutations are same for all observers. “Difference” does not mean that observer is measuring position and comparing with previous position when similar permutation occurred to find the difference. Rather, what it means is that during permutation A and an observer existed in position C and made an observation D. And during permutation W that was similar to A an observer existed at position C and made observation Z that was identical to D. Z and D are identical to the observer because he his limited by his “least count” limitations. If all observers are making same set of observations in both the permutations (A & W), then those two permutations are identical. Observers in these A and W permutations do not and can never communicate with each other across permutations. Rather, what is being stated is that since permutation A and permutation W are similar beyond all observers’ observable limits, all observers in those two permutations must end up making the same observations.

Even if space is continuous, difference between two permutations will become less than any less arbitrary limit as we shall see in this chapter. That means all observers – since they can make observations only up to a finite limit – will be observing same permutations in the universe.

We know universe only through observations and observers. “Actual” positions of objects – are they “exactly” identical in such similar permutations as A and W or merely appear identical due to observes’ limitations in a continuous space universe? This question is metaphysical, because we can only know the universe through observers and observations reported by them. What is “actual” and “exact” if no observer can measure it? For all observers of the universe, those permutations are identical. (Idea of “exactness” and “actually” beyond the realm of observations and observers is metaphysical.) In this way, it is shown that even if space is continuous, matter and energy can permutate in finite number number of ways in finite space. This finite number cannot be known, and it is not just dependent on quantity of space and matter but also on accuracy of measurement of the most accurate way of making observations of positions in the universe. (Theoretically speaking, if all energy of the universe is carried by just one photon, the wavelength of that photon is the most accurate way of making observations of positions in the universe. This does not leave any room for observer to exist but does give an absolute minimum length possible in the universe. Amount of time that this photon takes to travel this length, its time period, is the minimum time interval possible in the universe.)

The above argument is a side step from the assumption of quantized space. If space is quantized, total permutations possible in finite space will be finite.

Time as interval and time as permutation

Time is known in two ways: one as interval, duration or count, and other as permutation. Time as interval is measured in terms of a count that happened between two events. For example, number of times seconds hand of a clock ticks between two events. All measurements of time as interval can be understood in this manner as unit of time itself is defined as a measure of count or number of events: when 9,192,631,770 number of times a cesium-133 atom’s light vibrates (frequency), it is one second. Time’s nature as measure of interval is well known. It is the other way of understanding time that is not interval at all but rather how all observations are made including that of time as interval that is the focus here. All observations are observations of permutations. Time as interval is no exception. Rather, this understanding of time – time as permutation – is how time is actually measured by all observers anywhere in the universe. When we measure time, we look at a clock, its arrangement and that tells us time – a permutation. We compare this time with another time stored in memory and calculate interval, but that memory is also part of the present permutation. Thus ‘time as interval’ manifests in one permutation to observers as we don’t see the past permutation, but only its evidence in memory. Thus, space remains, matter remains, matter changes its arrangement in space and that gives rise property of time to observers with memory. Time does not exist independent of changing arrangement of matter in space. These ideas have far reaching implications on understanding basic nature of the universe, as it constitutes only space, energy and energy changing its arrangement in space.

Permutations

A permutation is any one possible arrangement of a given number of things. Therefore, set of all permutations for a given number of things is nothing but arrangement of things in every possible order. In other words, repeatedly interchanging positions of things with respect to one another until all the possible permutations are accomplished. To understand it still more simply: if one keeps on changing order of given things until one fails to find an arrangement that is different from all the previous ones; any one of those arrangements can be referred to as a permutation, and set of all the arrangements (or permutations) may be called all permutations for those given things.

The following examples will make this concept more clear. Consider two balls of different colours, say of red and green. They can be arranged in a single row in only two different ways.

Arrangement 1 R G

Arrangement 2 G R

FIGURE 3.1

If there are three balls of different colours, say of red, green and blue, they can be arranged in six different ways.

Arrangement 1 G B R

Arrangement 2 R B G

Arrangement 3 B R G

Arrangement 4 G R B

Arrangement 5 B G R

Arrangement 6 R G B

FIGURE 3.2

The following table shows the number of all possible permutations in a single row and number of things.

Number of things Number of all permutations in a single row

1 1

2 2

3 6

4 24

5 120

6 720

7 5,040

8 40,320

9 362,880

10 3,628,800

TABLE 3.1

We see that a mere ten things can be arranged in a single row in more than three million different ways. Just look around and know that there exist astronomically large number of permutations in which things in your vicinity can be arranged. The numbers are big, they are so much big that one cannot comprehend them. But the point not to be missed is that they are finite. Even if one takes a hundred things and tries to arrange them in all possible permutations one should come to an end of it. (But for that person’s life--it would end much before the permutations.)

For all the previous examples we considered relative arrangement of things in a single row to finally conclude that permutations, though however large in number, are finite. But in reality arrangements of things are not restricted to a single row. To understand this, consider the first example of the two balls again:

Arrangement A R G

Arrangement B R G

FIGURE 3.4

Both the arrangements--A and B--are essentially the same: red ball is on the left of green ball in both. But it is quite evident that the balls are farther apart in the arrangement B in comparison to the arrangement A. This makes the two arrangements different from one another, a difference which was not considered earlier. Thus any change in distances between things too leads to new arrangements. And this change in distances need not be so large that it can be deciphered by naked eye only. Any alteration in position of things, however slight that may be, leads to new arrangements.

Thus we see that a permutation not only depends on relative arrangement of things but also on distances between their positions. Now, as a last example, consider a particle in finite bounds of space. Out of many ways in which the sphere can be positioned, consider any two possible positions: A and B.

FIGURE 3.5

One can find another possible position between A and B, call it C.

Figure 3.6

Between A and C there can be D, and between A and D there is E and so on. Similarly, positions can be spotted between any two possible positions. As one keeps on spotting more and more possible positions distance between neighboring spotted positions decreases. When number of spotted positions become very very large the distance between neighbouring spotted positions correspondingly becomes extremely tiny.

FIGURE 3.7

If space is continuous, then lower limit to tininess in distance is zero. But zero distance between neighboring positions signifies that they are actually the same position. We shall see that if space is continuous even then permutation can become so identical after finite permutations that no observer will be able to tell the difference between permutations as the deviation will become less than all observers’ least count.

To understand how permutations become observably finite when space is continuous, a hypothetical concept of ‘closeness’ is introduced. That is, if separation between any two positions is less than some very small distance then those positions can be considered as physically ‘too close’. By ‘too close’ it is meant that distinction between ‘too close’ positions is unfathomable to an observer. (The concept of ‘too close’ is no different from least count of observations.)

So if any two positions are closer than the ‘too close’ limit then it becomes needless to refer to them as distinct positions for that observer. They are too close for that observer. To illustrate this concept consider any position A. Consider an unrealistically high value of ‘too close’ limit, say two centimeter. So any two positions which are closer than two centimeter should be indistinguishable. Such a large value of ‘too close’ limit is being considered only to make the illustration clear and conceivable. Thus all the positions within the range of two centimeter of A are supposedly indistinguishable from A.

FIGURE 3.8

In example of figure 3.6 we tried to find numerous positions in which a particle can be positioned within finite bounds of space. We noticed that as one keeps spotting more and more number of positions, distance between neighboring spotted positions decreases. When number of spotted positions become very very large, distance between neighboring spotted positions correspondingly becomes extremely tiny. But according to the concept of closeness ‘too close’ positions are indistinguishable (depending on the value of ‘too close’ limit for an observer). That is, the positions that are closer than ‘too close’ limit cease to be distinct for that observer X. So all positions closer than two centimeter are supposedly indistinguishable for observer X.

Out of many ways in which a particle can be positioned consider any two possible positions-A and B

FIGURE 3.9

Respective ranges of closeness of A and B are shown in the following figure.

FIGURE 3.10

Another position (call it c) can be spotted between A and B. But for C to be distinctly different from A and B it should not fall within the ranges of closeness of A and B. Because if C is inside the range of closeness of A, then it will be ‘too close’ to A. That is, it would be as if one is referring to the same position again for observer X. Therefore, for C to be distinct it has to be spotted anywhere outside the ranges of closeness of A and B.

FIGURE 3.11

And C too shall have its range of closeness. Hence figure 3.12 follows.

FIGURE 3.12

Now a fourth position (call it D) is to be spotted. But for D to be distinct from A, B and C it has to be outside their ranges of closeness. Thus D is spotted anywhere outside the ranges of A, B and C.

FIGURE 3.13

D also has got its own range of closeness.

FIGURE 3.14

In the same manner, if any other distinct position has to be spotted, it has to be outside the ranges of closeness of A, B, C and D. For that matter, any position is distinct only if it does not fall within the range of closeness of any other position. So if any new position which has to be spotted, for being distinct it should necessarily be outside the ranges of closeness of all the previously spotted positions.

Following the above criteria, if one keeps on spotting distinct positions finally something interesting happens. A stage comes when simply no space is left which does not lie within the range of closeness of some already spotted position. After this stage it becomes impossible to find any more distinct positions as all the space gets filled by ranges of closeness of already spotted positions. So if any new position has to be spotted, it cannot be but within the range of closeness of some already spotted position.

FIGURE 3.15

Such a position won’t be distinct, but it would be ‘too close’ to an already spotted position, that is, it would be as if one is referring to the same position again for observer X. So no new distinct positions can be spotted. The conclusion derived through these figures is: one runs out of distinct positions in finite space. But there is no reason whatsoever to assume two centimeter as the ‘too close’ limit for all observers.

Now let’s halve the value of ‘too close’ limit, making it one centimeter. Now positions which are nearer than one centimeter are considered as not distinct. Repeating the same procedure of spotting distinct positions, this time one can find much more number of distinct positions than before. But eventually the same stage arrives: all the space gets filled by ranges of closeness of already spotted positions, thus leaving no place for any more new distinctly different positions.

FIGURE 3.16

But the same argument stares again: even one centimeter is not the ‘too close’ limit for all observers.

We notice that as value of ‘too close’ limit is made smaller and smaller the number of possible distinct positions correspondingly become larger and larger. If a hundredth part of a millimeter seems too large make it billionth part or trillionth part or trillionth part of even that and so on, the conclusion continues to loom large. The deviation between latter positions and the former ones is bound to become smaller than any assumed non-zero ‘too close’ limit. Irrespective of how small may one assume the ‘too close’ limit to be, a stage must come after finite positions when newer positions would become indistinct from the previous ones for all observers, it would be as if matter is occupying the same place again.

The conclusion is independent of any assumed value of ‘too close’ limit. So one can freely assume the ‘too close’ limit to be as much close to zero as any observer’s imagination allows. Eventually after finite permutations the deviation between the latter and the former positions is bound to become even smaller than arbitrarily small.

Thus the eventual deviation is less than arbitrarily small. Because whatever ‘too close’ limit we imagine, after finite permutations the deviation between the latter and the former positions is bound to become less than that. Therefore after finite permutations it will become smaller than limits of observations for all observers. Thus the imminent would happen, and then the latter positions would become completely indistinct with respect to the previous ones for all observers and therefore they will be identical for all observers.

This is a mathematical conclusion true for all observers. The given condition is that space available to place objects is finite. All observers make observations of only finite accuracy and there exists no observer who can make an infinitely exact measurement of positions. The more accurately an observer tries to measure position, he uses light of smaller wavelength, that is, light of higher energy. In order to make “exact” measurements an observer will have to use light of zero wavelength. All energy of the universe will be insufficient to produce such light. This shows exact observations are physically impossible. Not only this, to store information about an “exact” observation of position, there won’t be enough memory available in the whole universe. The idea that exact positions exist for particles even if they cannot be observed nor stored, is a metaphysical one. Such exactness is elusive for all observers. (This idea is different from Uncertainty principle in that it only deals with positions and whereas that principle deals with position and momentum.) Moreover, since universe consists of finite energy, there must exist a maximum upper limit for energy that a photon can carry, such photons wavelength will be the minimum length measurable for all observers. Therefore, there must exist a finite limit to which observers can measure positions. Once that limit is reached, positions will become indistinguishable for ALL observers.

We considered just one particle and tried to position it in unique positions. Had there been two or for that matter any number of particles, the conclusion would have been the same. Permutations in finite space are finite irrespective of number of particles. This conclusion is valid even when one considers that in finite space particles can exist in more than one position at once. Permutations and combination allowed will be finite for finite particles in finite positions even if they are allowed to exist in more than one position at once. Finite permutations in finite space also overrides that entropy of a system must keep increasing, because in this system only finite states are possible and therefore entropy cannot keep increasing indefinitely.

Orientation of a particle is also a way to alter permutation without apparently altering the position. In the figure 3.17 a particle has been rotated by 90 degrees about an axis, thus the particle is now in a new permutation though it may be in the same position.

Text Box: A

Figure 3.17

However, on closer look, the positions of everything about this particle are not the same. Any particle that can be observed by an observer to be having an altered orientation, the very manifestation of altered orientation is due to altered position of sub-particles of that particle. In the above figure, the particle’s orientation change is made observable by way of change of position of particles in top left ‘A’ to have come to different positions. This shows that all particles are not in the same position, which manifests as change in orientation. Once all particles constituting the main particle are in the same position, the orientation of that particle is automatically the same as no manifestation of change in orientation shall be observable to any observer. Therefore, identical permutation of positions must also lead to same orientation of all particles in that system. Like orientation, any change in any property when positions are apparently the same can be traced back to altered positions of some particles in that system. Observers observe only positions; a change in orientation is nothing but observation of change of position of some or all particles of that body. (Another way of making orientations finite for a particle is: change in orientation is a measure of angle, and the smallest angle that can be measured by any observer is equal to minimum measurable length in the universe divided by maximum length possible in the universe. Minimum length is discussed above as wavelength of the most energetic photon possible in the universe – which is finite. Maximum length is finite in a system that is spatially finite. Therefore, the smallest angle that can be measured by any observer is also finite. Therefore, number of different ways in which a particle can orient itself is also finite. This way of showing that maximum possible orientations of a particle are finite, is redundant as change in orientation is nothing but a manifestation of change in positions, we know that number of possible positions are finite, that makes change in orientations a subset of change in positions. Hence, if number of possible positions is finite, one need not consider orientations separately as they also become finite automatically.)

This conclusion that only finite permutations can exist in finite space is independent of everything else that one can think of.

Hence for any non-zero limit to closeness (arbitrarily small alpha), after finite permutations, the permutations will start happening which are deviating from a previous permutation by less than alpha. And there must exist a value for alpha beyond which all objects will have positions so much like a previous permutation that the deviation will become less than measurable limits of all observers. Therefore, no observer will be able to distinguish between those permutations.

We already know that speed and direction of motion of a particle too are measured by observing permutation: memory of the observer (previous position of particle and previous clock time) and present clock time and position. This means even as an observer tries to measures position and velocity of a particle, at any given time he is observing positions only. These positions are positions of the particle in question and particles storing information in memory. The main point is (observer being within the system hence made of matter of the system whose permutations are in question) that in order to show for a permutation to deviate by less than alpha from a previous permutation, (alpha being small enough that all objects will be having positions and velocities so much like a previous permutation that the deviation will become less than all observable limits) one need not bring velocity in the picture as it is incorporated in positions of particles of that system. That is, if all particles’ positions are arbitrarily close to a previous permutation, their velocities too are arbitrarily close. Therefore, if positional deviation between two arrangements can be shown to become arbitrarily small, by implication one would have shown that velocity deviation and all other observations’ deviation is also arbitrarily small.

What is important to know is that observer is within the system and not outside. For the understanding of universe, all observers must be inside the system. When the observer is inside the system and measuring velocity, his memory and the clock are part of the system. Observer is observing from within, the previous positions of particle and previous clock times that have been measured are in his memory, and part of the permutation. So is the present position of the particle being observed and present positions of clock needles. Therefore, the velocity of the particle is completely defined by positions only. In the same manner it can be shown that all observations, no matter how complex, are defined by present positions only. (This is not an interpretation, but this is how all observers are actually making observations. Observers are either observering memory in present or objects in present and never past.) We can fix a non-zero alpha arbitrarily small and show that deviation between two permutations is less than what is detectable by any observer. All the particles’ positions - in memory, in clock and others will be indistinguishable from another permutation. (Intervening these two permutations is only a finite number of permutations.) These two permutations though happening after a long sequence of distinct permutations, are now the same. All observers will be making the same observations and all clocks will be showing the same time.

This conclusion of finite permutations is independent of cause and effect, it does not matter what sequence of arrangements is followed. If space is finite, one need not track the sequence of permutations to conclude that permutations will start repeating. All particles must eventually be in the same position. Therefore, all other properties, will also become the same. This does not violate uncertainty principle, as the observer is not measuring position or momentum of the particle to show that it is in the same position. An observational confirmation is not required for acceptance of this principle, small scale experiments, like arranging three balls in five slots and finding that this can be done in finite number of ways only is good enough observational confirmation. Finite permutations possibility in finite space will ensure that that will happen for all the particles regardless of it ever being confirmed by any observer. Once all particles are in the same position as before, all observations happening in the universe also become the same because all observations spring from permutations. Observations including about uncertainties about positions, gravity, electric and magnetic fields, waves, there are no exceptions because all these properties are described and measured by arrangements only by all observers. All aspects of universe manifest through arrangements of objects and arrangements of memory. Which arrangements are part of memory and which not, are observer’s personal volition – essentially they are both arrangement of particles. We have already seen how this happens in the case of velocity, this can be shown to be the case for all properties about particles without any exception. A permutation is superset of all observations in the universe, when a permutation is the same then all in the universe is the same.

CHAPTER 4

Time like proverbial ether

Our contemporary understanding of time is reminiscent of pre-relativity space. Space was assumed to be permeated with ether which stands regardless of any objects’ motion within the universe. The space-ether was therefore the ultimate stationary frame which was omnipresent and all motion in principle can be measured with respect to it. In the same manner, contemporary time has a beginning, that provides a reference for all other events in the universe. There is an apparent notion that time as a dimension “flows” forward regardless of arrangement of any matter or energy contained in the universe: when twenty-four hour clock is showing the same time again, the time has moved forward by twenty-four hours even though the clock is showing the same time. Time is not actually the same because the observer-clock system is not isolated, the observer knows that calendar and sun are clocks which track much larger intervals of time. This does give an impression of time “flowing” forward because there are always other ways to measuring longer times. But in a system where there is no way of tracking more time than maximum allowed by that system, for such a system time’s ether-like nature will cease and time will be the same for all clocks and observers.

Finite matter and energy, in whatever form and quantity, can permutate in finite number of ways in finite space. This was the final conclusion of the last chapter. As the reasoning preceding the conclusion essentially revolved around positions only, the conclusion should be applicable to any entity that pertains to positions. Matter was just the medium through which the conclusion was reached and conveyed while it was only the positions that mattered throughout the discussion in the last chapter.

And all observations pertain to positions only.

Based on the criteria that there is no beginning and there cannot be infinite time before an event it was concluded in chapter 2 that the universe is self-contained, finite and without any boundary. Universe is always changing arrangement. Changes are going on on the surface of the earth, in oceans and inside the earth. Changes are going on inside the sun and stars. Solar system changes as the planets and their satellites change positions. Galaxies revolve around themselves as they move further apart.

All changes that occur in the universe involve energy. All it has is energy in space and nothing else, it could be in the form of matter or electromagnetic radiation or in any other form, known or unknown. Change is nothing but alteration in arrangement of energy in space. And whatever that exists, it has got some position in space at any time. This means that all that exists, that is, all the energy of the universe, pertains to positions. That which does not pertain to positions in space is unobservable and therefore meaningless. All science is based on observing present positions of energy and finding the best way of predicting how the energy will rearrange in new positions with time, or to understand past arrangements by knowing present ones. In other words: cause and effect.

Accepting the universe is finite in extent with finite energy in it and also that ‘changing universe’ means that arrangement of the energy is changing in space. A new arrangement of the energy is different from previous ones, and this alteration in arrangement of the energy of the universe is governed by laws of nature. From the last chapter we know that permutations in finite space are finite. This conclusion is free of all constraints and is inescapable. The universe, as it changes grants energy newer and newer permutations in space. Going by the last chapter’s conclusion this cannot go on up to infinity. After some finite number of permutations, finite space of the universe will run out of distinct permutations even if alteration in permutations were not governed by any laws and is random. What will happen after all the possible permutations are over? Should it not keep changing even after that? The answer is yes. Change is the perennial property of the universe because it cannot have a beginning so it must keep changing (or permutating) even after all the possible permutations have been realized. But how will it change when there are no new permutations possible? What will come beyond?

The universe, as it is changing, will keep changing spontaneously and endlessly. Permutations will keep coming and going but, as number of distinct permutations possible are finite, a stage will come when all distinct permutations will become a passe and then no other way will be left but a spontaneous repetition of a permutation. The reason is though given in detail in the last chapter, it can be put more nascently as: it is an inevitability in an ever-changing finite universe because the number of permutations possible are finite and also the universe must keep changing even after all the permutations are over. So one of the previous permutations must get repeated, and the repeated permutation will be the same as the original permutation. Thus, the state of the universe will become the same as it was when the original permutation was there.

Since the state of the universe shall become the same as a previous original permutation, the effect of the laws of nature will also be the same as before. Thus, due to this effect the universe shall be undergoing the same sequence of permutations which were there after the original permutation. But this is not necessarily true. As concluded in the last chapter, even if sequence of permutations is completely random, the number of possible permutations still remain finite. So to conclude that the sequence of future permutations will also become the same (as those followed the original permutation) when permutation is same again is not entirely justified. But for the present it is accepted to be the case. It will be discussed in detail in the next chapter. In any case, sequence of permutations – regardless of whether it is followed or whether they happen randomly do not affect the larger conclusion that finite space allow only for finite permutations after which permutations must repeat.

After finite time the same permutation will be reached again and the same sequence of permutations shall reappear. All these permutations will be identical to the previous ones for all observers in the universe.

Thus, it is inevitable for the universe to fall in a cycle of same changes happening again and again. All the permutations that come after the original permutation will keep reappearing again and again because they all fall in a cycle. But what about the permutations which come before the original permutation? They won’t be able to resurface ever again for they don’t form a part of the cycle.

But why nature would select a particular permutation and go round

Figure 4.1

about it forever, and shun others as lost forever? Or in the first place what is the location of the original permutation in time, does it lie in future or in past? If it lies in past then we are already in the cycle ! But how can that be said? What reason have we got for the original permutation to be in the past? Assume that the original permutation lies in future. So after some finite time the original permutation must come, and go--only to resurface again after some more finite time. This process will go on and thus the universe will fall in the cycle but without the present permutations being part of it because the cycle will start in future. Once fallen, there is no way the universe can come out of the cycle. In this manner the future of the universe is, in principle, deciphered for all times to come.

Figure 4.2

But all past is dangling not as it is not part of this cycle. We know that after some finite time the universe runs out of distinct permutations. Now imagine very very long time back in past. Whatever permutation be at that time, the universe had been changing then (and before that also), and after some finite time the universe must have run out of distinct permutations which would have surely resulted in spontaneous repetition of some initial permutation. Hence, the universe must have fallen in the cycle – but this time it is in past! This means that the original permutation lies in the past.

Thus, the axiom of ever-changing universe shows that the repetition of permutations is already in progress! That is, the original permutation lies in the past and not in the future. Now figure 4.2 can be redrawn as:

Figure 4.3

But now extremely archaic past is dangling in the same way as past was dangling in figure 4.2. With the same reasons (that is, the axiom of ever-changing universe and the conclusion of finite permutations) it can be shown that the original permutation got repeated still more time back in past. That is, the cycle started even more time back in past. But there is no limit to the changing past. So there could be even more archaic past dangling, asking for further thought.

Figure 4.4

It is a game without an end. Because whatever time it be in past, there would still be time before it and the universe would be changing even before that. And then by the reasons we show that even that past should also be part of the cycle and the original permutation lies somewhere still further back in past. But as we try to move further back, still more past springs up! We notice that the cycle is as if it is rolling on the past and trying to wrap it all on itself but the past is apparently endless.

Endless past

Figure 4.5

Our search for the original permutation, our curiosity to know the beginning of the endless dangling past signify many a great follies of human mind which still remain nestled in our understanding of the cosmos. It is time to cut that dangling past as umbilical cord be cut when a newborn breathes its first. There is no beginning, nor there will ever be the end to universe. Any time it be, by knowing the universe was changing before that time and using the conclusion regarding permutations, it can be shown that the cycle has started before that time. The folly is that we are wanting to know a beginning of the cycle.

Figure 4.6

Some finite passage of time makes state of the universe the same as before. These same states of the universe, though being the same as all clocks show the same time and all observers make the same observations, are separated by some finite duration. If these states are the same, then we ought not refer to them as two different ones but as being one and the same. But since they occur at different times of the universe one might object to it. After all how two states, however same they may be, be one and the same when they occur at different times? This argument of their occurring at “different times” is totally null and void unless we consider time to be ether-like that it keeps moving forward regardless of arrangement of energy in space. After some finite duration it is time of the universe which becomes the same as before. A particular permutation of energy in the universe pertains to a particular time of the universe. When a permutation reappears, all conditions of the universe become the same as before and hence time too becomes the same, all observers are making the same observations, all clocks are showing the same time. Hence these same states are occurring at the same time. Now we are no more talking about same times and same states, it is actually the same time and the same state.

After some finite passage of time, time of the universe becomes the same as before. What does this mean? This means that time is finite without a beginning or end. The futile search for the original permutation shows that time was never had a beginning, nor an end. It was always here, reappearing “again and again”, showing itself to us mortals, every time our time comes, “as if” it has come for the first time! [“Again and again” is double quoted because each time it comes, it comes only for the first time; it comes only once, as will be explained.]

If time is not the same when permutation is same, then those identical permutations are not identical: there one property that is different – which is time – between these two permutations. Then the question will arise how do we detect this time that is different. We know that time is only measured with permutations, so no matter how an observer tries to detect this ether-like time that is different between these permutations, since permutations are identical, all observations made will also be identical. Thus, ether-like time has no observable relevance. Time only manifests through permutations, when permutation is the same, time is also the same. Ether-like time that keeps moving forward regardless of permutation of objects is meaningless. Time is always a representation of a permutation and if permutation of universe is the same, time of universe is the same. This makes time finite. Finite time and permutations do not mean that time is “repeating”. Repetition of time would again make time ether-like, that somehow there exists a mysterious way to show that a permutation-independent-time exists, in other words, there exists a way of theoretically conducting a thought experiment to show that the same permutation is happening “again”. The permutations are finite, but when we say they “repeat” there must be at least one way to tell them apart – otherwise they are one and the same. In order to establish “again-ness” of time, there must exist a way of retaining information about the last identical permutation so that the two identical permutations are compared and declared identical by a super-observer. But there is no cheat counter/information-tracker that can tell even a super-observer that it is happening “again”, the information of all counters will have to become the same for a permutation to resurface and therefore the information about “again-ness” must be lost in order for the permutation to become the same. A time happens only once, never again. Because if it is happening “again” that means those permutations are in some way different. It is loss of “again-ness” of permutation that makes it the same time in the true sense in the universe. A time happens only once for all observers because no observer can detect it happening more than once. Hence the “again-ness” of time is a misnomer. A time happens only once, and it is finite with no beginning or end.

Oval: Time

Figure 4.7

Thus , the universe had always been changing and yet there is finite amount of time before all events . Because after some finite time, time of the universe is the same. The ever-changing universe does not mean that there has to be infinite time before and after all events and that time extends to infinity in both the directions. Time derives its existence from changes happening in the universe. Time pertains to state of the universe, and now we know that there are not infinitely different states possible – they are finite – so time is also finite. Cosmos is nothing but a finite series of changing permutations of energy. Hence, time is finite, and cosmos is ever-changing without there being a beginning and yet there is finite time before all events.

In chapter 2 we discussed a universe that is stagnant, in which no change is occurring, shall always remain stagnant. As nothing is changing in that universe, there cannot be any cause from within which can induce it to change. So a stagnant universe is stagnant for always, its past, present and future--all being the same. It is important to note that a stagnant universe is for always the same. This means that a changing universe can never stop changing because if it does it will violate the idea. In an unchanging universe the concept of time makes no sense. On these arguments the conclusion derived was that the changing universe shall always remain changing. The universe changes, therefore, time is. With change, events happen in the universe. But an event can happen only if there is not infinite amount of time before it. Because if there is infinite amount of time before any event, for however long time the universe waits for the event, it would still remain infinite time away. The chasm of infinity cannot be bridged. So it was concluded that there cannot be infinite time before any event. Both these ideas are totally compelling, and any acceptable cosmic theory must explain them both.

If one looks at the two ideas independently, they are totally compelling, but when both are looked in the light of each other, they conflict bitterly. While the universe should always be changing, there shouldn’t be infinite time before any event. If you accept one, the other stands defeated, and yet each idea is equally justified in its own right. Which one to accept? If one accepts the idea of ever-changing universe, the problem remains as much unresolved as it can be. Popularly, the other idea has been accepted and contemporary model of universe has a beginning, which states that a changing universe came about from an unchanging universe.

Although in the chapter 2 I mentioned the apparent conflict between the two ideas (of ever-changing universe and there being finite time before any event), I accepted both as true. As to why I accepted both the ideas without giving any reason, all I can say is that there was no reason whatsoever to drop any of the two. I see no harm done if I stuck to both the ideas, for even if there was any conflict, it was just a misconception, a confusion between time and change which has since been resolved. Based on these two ideas it was concluded that space is finite and without any boundary. When the unconditional conclusion regarding finite permutations was applied to finite space of the universe, it was realized that there is no way space is finite and boundaryless and time is not. This led to the conclusion of finite time without a beginning or end, and also to a resolution of conflict between those two ideas.

Even if I’m totally justified in upholding both the ideas and even if it might seem that the conflict has been resolved, but there are still a few impediments left in the resolution, albeit minor ones, which will be dealt with here. In the chapter 2, based on the conflicting criteria, all the possible histories of universe were considered, and were accepted and rejected accordingly. All of them were rejected except the fifth history. But the reasons for rejecting the third history were not given. According to the third history: The universe was smaller and smaller till it was of some fixed finite non-zero space in finite time in the past, and the universe was never smaller than that finite space . For all times before that finite time the universe was ever-changing within that fixed finite space until something happened from within which produced such an effect that the universe started expanding. Thus, according to the third history the universe was ever-changing within some fixed finite space before it started expanding. Also while discussing the fifth history we came across the possible explanation of the pre-nadir contraction of the universe, according to which prior to the beginning of the contraction, the universe was always of some fixed finite space and it was ever-changing within that finite space. That is, as the universe was changing in that finite space it stumbled upon such a happening from within which produced such an effect that the universe started contracting. Thus, according to this the universe was ever-changing within some fixed finite space before it started contracting. Just like the third history, this was also rejected in the second chapter and no reason was given for it.

It is worthwhile to notice that the third history and the possible explanation can be explained only on the basis that the universe was ever-changing in finite space. The reason for assuming the universe to be of always fixed finite space in the third history and the possible explanation is very simple: any deviation from this will alter their very nature and make them some other history.

Now we know that if the universe is ever-changing in finite space, the events must become repetitive because there are finite number of permutations possible in finite space. In both, the third history as well as in the possible explanation it is the basic assumption that before the universe started expanding or contracting (as may be the case) it was always of fixed finite space and was ever-changing within that finite space. So in that universe, which was always changing in fixed finite space, time would have become finite. Since all possible permutations get exhausted in finite time, if universe was always finite it means, there is no permutation possible in that universe which can permit it to start expanding or contracting. But when we say that it suddenly started expanding or contracting, which was not there in any of the previous permutations (because before that sudden expansion or contraction the universe was always of finite space), we are saying that the universe arranged into a permutation which was never part in its entire set of finite permutations – which is impossible.

So if the universe was of fixed finite space for always there is no way it could have happened that the universe started expanding or contracting. It should have always remained of fixed finite space. Therefore, both, the third history and the possible explanation, are invalid. The reasons for why I could not explain all this there and then in the chapter 2 are self-evident. The reasons for their rejection could not be communicated without going into the idea of finite occurrence of permutations in finite universe. The reasons I use to reject the third history and the possible explanation are only dependent on the idea of finite permutations, only that I could not communicate them earlier. Therefore my acceptance of finite space without any boundary at the end of chapter 2 is justified. Once this is done the conclusion of finite time with no beginning follows unconditionally.

For reaching the conclusion of finite and boundaryless universe we considered all the possible histories that the universe could have had. Based on the compelling, simple, but then conflicting criteria, first, second and fourth histories were straightaway rejected. I also expressed my inability to communicate the reasons as I rejected the third history and the possible explanation. Finally, only the fifth history was accepted and hence we concluded that the universe expands and contracts alternately. But as we looked at it form ‘curvature in space’ point of view, we inferred a universe that is spatially finite but without having any boundary. As I reached this conclusion I left few questions unanswered. I was justified in holding on to the conclusion of finite and no-boundary universe because without emphasizing the impact of the conclusion of finite permutations on the finite universe, I couldn’t have entered into the concept of repetitive occurrence of events in the universe and then explain that “repeat” of universal permutation is not a repeat but same time. Hence I could not have vindicated my rejections of the third history and the possible explanation. And therefore I could not remove objections to finite no-boundary space without going into finite no-boundary time. Their interdependence is so complete that I could not crack one without cracking the other.

CHAPTER 5

In chapter 4 it was mentioned that if universe is at the same permutation (as a previous one) then the same sequence of permutations must be followed after that. But why it must be so? It was also mentioned that even if permutations follow a random sequence the basic conclusion that ‘time of universe is finite’ stands. In this chapter we will see why the universe must follow the same sequence of permutations. In a way this idea goes against the grain of quantum mechanics – if no observer can ever accurately measure position and momentum of a particle, no observer can ever precisely predict the future. If no observer can ever precisely predict the future, it may be concluded that uncertainty about future is intrinsic to the universe. There is no known method by which is can be shown that although future events of universe are uncertain, the future is predetermined even though indeterminable. If universe is uncertain for all observers then it is intrinsically uncertain. (I have also used similar arguments in this work: if something is true for all observers then it is accepted as natural truth.) So then why it must be that permutations are required to follow the same sequence in a finite space universe?

To begin the explanation for why permutations are required to follow the same sequence in a finite space universe it is assumed/accepted that there is no such requirement. That is, it is possible that permutations at any point in time may follow a sequence of arrangements which are different from the previous ones followed after the same permutation. The following diagram shows this schematically.

Present

(or permutation X)

Figure 5.1

Figure 5.1 shows a permutation X, representing a time (say present) which when arrived can follow path 1 sequence of permutations. Or if this very permutation happens “again” it may as well follow path 2 sequence of permutations. Thus there are more than one distinct futures possible and it is completely a matter of chance as to which one will actualize.

However, it is important to keep in mind that at some time in future these two different paths must intersect. By “intersect” it is meant that although permutations of path 1 and path 2 are different, they can remain different only temporarily as in finite space only finite permutations are possible. To clarify further, “intersect” does not mean that these two paths are being followed by the universe simultaneously – not at all. What it means is that even though different futures are possible, no matter which future is followed it must comeback to the same present because only finite permutations are possible. To put it differently, regardless of which future sequence of arrangements is followed, they all will lead to a common permutation. This is inevitable as permutations possible are finite, even though they may be happening randomly.

Now we switch focus to that time when two different paths lead to the same permutation. What this means is that a time can be arrived by more than one pasts! Figure 5.2 schematically shows it. Permutation X can be reached by past 1 (path1) and as well as by past 2 (path2).

Figure 5.2

We know that at permutation X, regardless of past followed to reach this permutation, all observers are making the same observations. Previous positions of particles being observed are stored in memory of the observers. Because Past 1 and Past 2 are different, there must exist at least one particle that approached its position during permutation X by following a different path during Past 2 vis-à-vis Past 1. Now we switch focus to that particle and an observer in its vicinity and the time is that of permutation X. “Time is that of permutation X” means that the particle is now in its final position – common to both pasts – observer is observing it in that position and its previous positions are recorded in that observer’s memory.

In path 2, particle is now in the same position X, but on account of different path followed to reach this position, the observer’s memory becomes different, thus preventing it from becoming the same Permutation X.

Figure 5.3

Figure 5.3 shows this particle, that reached at final position X. It reached this position either by past 1 or by past 2. Let us assume, it followed past 1. This means, the observer recorded previous positions of the particle as A1, B1 and C1. This information about the previous positions is stored in memory of the observer and it forms part of the permutation X. If this particle approaches the permutation X from Past 2, the observer would have recorded A2, B2 and C2. But if recorded information of the observer is different between ‘Past 1 approach to X’ and ‘Past 2 approach to X’, then Permutation X (reached by Past 1) and Permutation X (reached by Past 2) – both are not same. The reason is: permutation X in one case is having observer with A1, B1 and C1 in its memory whereas in the other A2, B2 and C2. This means that even if we have the particle in the same position, it is observer’s information about that particle that makes the permutation anything but the same if the particle has not followed the same path to reach that position.

It can be argued that since the permutations can occur randomly, the observer can be storing information A1, B1 and C1 even though the particle “actually” followed A2, B2 and C2. This way permutation X is successfully approached by two pasts. But in one past, observer is storing incorrect memory; he is saying A1, B1 and C1 instead of A2, B2 and C2. Are we prepared to accept observer malfunction? If yes, then we cannot trust our own memory of past. Moreover, if observer is storing A1, B1 and C1 as path of particle whereas it “actually” was different from A1, B1 and C1, then this “actually” is of no consequence as no observer can detect it.

Particle followed path 2 to reach position X, but it cannot be recorded by the observer if the permutation X is to be same as one reached by path 1. Therefore, path 2 is an unobservable.

Figure 5.4

We should, therefore, cut out of all other paths to permutation X except A1, B1 , C1 and all other paths are impossible. The idea of observer is not that there must be a coherent detector present, rather the concept of observer means is that evidence of a particle’s path of approach exists in the vicinity of that particle, whether an observer is purposely recording it or not. If a particle approaches a position from a different path, the evidence of that path is there and it is this very evidence that changes the overall permutation and prevents it from being X. This shows that any given permutation can be approached by only one past. If we assume that particle has approached a position from a different path but no evidence of that path exists, then that different path is immaterial – we should only consider the path whose evidence exists. And evidence or memory is part of permutation – therefore there is only one past for one permutation.

Another way of explaining the concept of figure 5.3 is to consider a person example. Like the particle having two pasts approaching one position during X, assume a person having two possible yesterdays but only one today: in one yesterday he went to a library and read a whole book and remembered its contents when he returned home. In the other yesterday, he went to a beach and returned home. What would he remember today – would he know the contents of the book even though he went to the beach? If he went to the beach and still knows the contents of the book, what about all the people’s memories that he met at the beach? Would they remember him? No one from beach should remember him because today is a state with his visit to library in everybody’s memory. Thus all observers become unreliable if more than one past it allowed. As equivalence of figure 5.4, if nobody remembers seeing him in the beach, he himself does not remember going there but remembers his trip to library and remembers the contents of the book and library staff remembers him too then it does not matter what he “actually” did, he is considered to have been in the library and not in the beach. The “other” yesterday is entirely meaningless and impossible, as its mark is never left in any observer’s memory. There is no way two pasts can be shown to lead to one present.

Why we had figures 5.3 and 5.4 in the first place: we had them because we assumed that more than one futures are possible out a single present. And in finite space universe, due to finite permutations, these futures must lead to a common permutation. It is imminent for these futures to lead to a common permutation. But if we switch focus to this common permutation X, we see that it is impossible for one permutation to have more than one past paths. A permutation can be approached by only one past. But more than one future necessarily lead to more than one past for permutation X – which is impossible. This means that more than one future is impossible. Which means, permutations must follow only one sequence of permutations after one time and more than one future is not possible even though the future remains unpredictable due to the limitations of the uncertainty principle.

In this way it can be shown that even if future remains unpredictable, uncertainty is not intrinsic to the nature of universe. Finite space not only makes time finite without beginning or end, it also shows there can be only one future. Postscript: In 1983 Jim Hartle and Steven Hawking proposed no boundary model of the universe. (Also known as the no boundary proposal.) This was also mentioned in page 144 of latter’s bestseller 'A Brief History of Time'.