When talking about the Universe and our infinitesimal place in it, it is unavoidable to talk in metaphors and allegories. After all...Can we really connect anything with concepts like ‘infinite’ or ‘boundless’ or ‘world-line’? And that most useful tool, language, has never been honed to describe the terminology used by cosmologists and quantum physicists. Likewise, in the following I will be using metaphors but at the same time trying to point out when we have reached the limitations for their use. A lot of unnecessary confusion stems from authors riding their metaphors for too long. Let me give you an example:
Astronomers have an understandable habit of talking about "penetrating into the beginnings of the Universe" or "going back in time" as if they are really going somewhere when they sit in front of the telescope watching the night sky. When they watch a planet which could be several astronomical units away (one astronomical unit equals the distance from the Earth to the Sun), they will say that this is planet X when in fact what they see is how planet X was maybe 20 or 30 minutes ago.
And if they leave our own galaxy, the Milky Way, and look at the nearest neighboring galaxy, the Andromeda galaxy (which is the only galaxy apart from our own that can be seen with the naked eye), 2.4 million light-years away, they will tell you that this is the Andromeda galaxy even when they know very well that "This is how it looks to us now". We do not know now nor ever can know what has happened to it since the light from its billions of stars was emitted as a spherical shell towards the rest of the Universe and from which we only receive an infinitesimally small fraction.
What is it we see in the telescope? We see an open history book of the part of the Universe that is accessible to our telescopes. It is a history book served smack in the eye; unlike ordinary history books which we have to read from beginning to end, this cosmological history book gives us everything there is to see in one single view. You may think of yourself as centered directly underneath an infinite number of hemispherical transparencies stacked on top of each other, where the farthest one shows the observable Universe a few hundred thousand years after the Big Bang when the first light in the form of photons escaped from the primordial plasma (see below) , and the nearest one displays the nearest object that the telescope can focus on.
This stack of transparencies whose total history covers nearly 14 billion years comes to you as one single transparency, namely in the retina of your eyes or, more correctly, in the visual center of your brain. Outside this the Universe ceases to "exist"! Let's pretend that you watch the Sun through a suitable filter. Are you really watching the Sun? No, as we know, it has taken the light 8.3 minutes to reach Earth. When you see the Sun, the image is already more than 8 minutes old. Anything can theoretically have happened to the Sun since it dispatched the light waves that you receive 8.3 minutes later on your retina in the form of photons; if a black hole, hovering above the ecliptic, sneaks in behind the Sun and then devours it, we won't know until 8.3 minutes later. There is no physical means of getting a warning: Einstein showed that no body can move and no message be transferred as fast or faster than the velocity of light in a vacuum.
This is trite, you may say. Furthermore, the astronomers and geologists tell us that the Earth has moved around the Sun for about 4½ billion years (Gyr), so it would be extremely improbable if a Big Sun-eater should suddenly snatch the Sun. But in principle we know nothing about the Sun just now. I will come back to this strange concept of “now” in a minute. The further we “go back” in time the less we know of the state of the Universe there now.
There are also the practical implications to consider: Even if we or our spaceship could travel at a velocity near that of light the news brought back after a lifetime of round trip voyage to distant spaces and back would simply be old hat, and the spaceship would only have penetrated into about two thousandths of the diameter of our Galaxy which measures about 80,000 light-years (ly) and which is only a medium-sized galaxy among the billions of other ones.
We may carry the argument further (or "closer" might be more appropriate); we do not know anything about what is happening on something as familiar and close as the Moon at this moment. All news from the Moon reaches us with a delay of just over one second. But now we are almost “down to Earth”, because for all practical purposes this is simultaneity. However, somewhere we will have to place the watershed between what is “now” and what is “past”.
However, the delay in the propagation of light gives us a great gift: The ability to study the evolution of the Universe practically back to its beginnings.
Suppose we could see William the Conqueror walking around as if on live TV, or if we could see the battle of Trafalgar on CNN! That would be possible. It would only require the fulfillment of a couple of conditions. William would have to have lived on another planet about 945 light-years away and the battle of Trafalgar taken place on a planet about 196 light-years away. There would have to be a camera crew present to record and send the happenings from the planet and out in the Universe.
Then William and Nelson would act simultaneously seen from the Earth, and we would be able to zap from William to Nelson and back. Thus we would be able to download historical events from different planets and their cultures; it would be an open, living history book for us. Our descendants in 200 years would be able to follow the final chapters in events.
This kind of ”live” history-recording is actually exactly what goes on every night in the observatories all over the Earth; the celestial postcards seeping down through the telescopes come from galaxies several billion light-years away and up to the light we receive from our nearest celestial neighbor, the Moon. A star at a distance of 200 million light-years shows us how it looked 200 million years ago, and how it looks today can only be seen in at least 200 million years from now. It is the astronomers' job to split up these cosmic postcards, determining the age, distance and other properties of the individual objects.
The Balloon and the Cosmological Principle
In popular scientific books on cosmology the Universe is often pictured two-dimensionally, like the surface of a balloon. This representation has some advantages; first, inflating the balloon mimics the expansion of space. If you paint numerous tiny dots on the skin of the balloon, each representing a galaxy, and then inflate the balloon, you can follow how the distance between the galaxies grows. If you put yourself on one of the galaxies, for instance our Milky Way, you will see the way nearby galaxies move away at moderate speeds while galaxies farther away recede at increasing velocities with the expansion of the balloon. The speed with which each galaxy recedes is called its "recession velocity".
Due to the continuous expansion, light from more remote galaxies is “stretched” on its way to us, thereby shifting its wavelength towards the red end of the light spectrum. This is called “redshift”, and by measuring that the astronomer may estimate the relative distance of the galaxy.
Another advantage of the balloon model is that it illustrates the general belief among many cosmologists that the Universe is endless but of limited size; on the surface of the balloon there is no end, no limit. If you follow a meridian, you will eventually end up where you started - but countless of billions years later.
And a final important analogy; the center for its expansion lies inside the balloon, and as our Universe is on its surface, this indicates that the "real" Universe has no center. Each location is equivalent to any other: no observer at any place occupies a point of vantage . This is the Cosmological Principle, and it asserts that the Universe at very large scales is both homogeneous and isotropic, that is, it is the same in all places and directions, and the laws of physics are the same everywhere.
However, the model is deceptive; it presents the false notion that one could step outside the Universe and get an overall view, a snapshot of it, and that you can put two fingers on two different places on the surface, giving you the notion of simultaneity.
Both notions are wrong in at least two fundamental ways: In the first place we know nothing about the Universe now. All we know is already history! Consequently we have no means of visualizing it, no means of putting two fingers on two different places on the surface . And the same may be said for any other location in the Universe. We easily forget that when we talk of a place, then we presume that it "exists" now. The key words are exist and now. Can anything exist when it is already in the past when we learn about it?
Secondly, there is nothing outside the Big Bang, so we cannot escape the Universe by stepping outside it. We are part of the Big Bang. Certain elements within each of us have followed its expansion right from the beginning. Take for instance hydrogen, the simplest and most abundant of the many elements in the Universe. Its subatomic constituents, the proton and the electron, were created during the first seconds after the Big Bang. And as water consists of hydrogen and oxygen, and as we are composed of 80-90% water, we all carry around several kilos of this 14 billion year old primordial matter (this being the latest agreed upon figure for the age of the Universe).
This should convey a sense of equality; the part of the Universe which is accessible for observation at any given position in space is only a tiny part of the whole. No place in the Universe has the advantage of being a center. Each has a different starry sky and a different cosmological history. But they can all trace that history back to one common starting point, the Big Bang.
As no light can possibly be older than the age of the Universe, this puts an upper limit to from how far back in time we can receive light even with the latest, giant telescopes. This limit is some 14 billion years (Gyr), and the galaxies and supernovae near that point are receding from us at close to light speed. However, there could well be celestial objects further out; they are just inaccessible to us.
While historians and archaeologists must dig the soil and scan through old documents because the events have already taken place, cosmologists and astronomers find themselves in the enviable position that the history of the entire (for us) visible Universe´ history is being displayed right in front of their eyes. However, astronomers cannot pick a specific star or galaxy, e.g. Proxima Centauri at a distance of 4.2 ly and say Now I want to see how it looked 30,000 years ago. They are forced to accept the image the Universe is presenting them with. And a spectator, e.g. somewhere in the Andromeda galaxy, will be presented with an image completely different from that of the astronomer.
But if our astronomer is not happy with what this image shows him, he may want to communicate. If he sends a light or radio signal towards, for example Proxima Centauri he will have to wait 8 years and five months for an uncertain answer. If he is more ambitious and emits a light- or radio-signal when in college he can reach stars about 20 light-years away and still get an answer before being pensioned. The Milky Way has a diameter of about 80,000 light-years so he will be communicating over a distance of merely 1/4,000 of our galaxy.
To lend support to these points I have made a crude two-dimensional model of what our Universe looks like, based on a hybrid of two generally accepted, possible cosmological models, the spherical model and the flat .
In order to do that I have used the figures in table 1 to make a model of the Universe at 32 different stages of its expansion, beginning with the Big Bang and incrementing by 250 million years (My) the first 2 Gyr and ½ billion the next 12 Gyr until today. The age 5 Gyr has a special significance to astrophysicists and cosmologists because it is the point in time at which the redshift z was 1 and the Universe was half its present size.
In the appendix I explain the equations and the assumptions used to calculate the values in the table.
Imagine the entire Universe pasted on the surface of a sphere. This little trick of bereaving the Universe of one of its 3 spatial dimensions makes it easier to visualize the often-quoted statement that the Universe has a limited size but no edge, just as an ant can continue crawling on the surface of a football forever without falling off an edge.
Now, imagine we further simplify the Universe throughout its expansion since the Big Bang singularity (which had no extension) until today as a cross section, where each stage of expansion is represented by a circle. As radius we will use the corresponding Scale factor Rt in table 1. We now have 32 spheres, the last of which represents the Universe now. For my argument, I shall only need the upper right half of the spheres, from the part above the Scale axis.
I will then follow a light pulse - a photon - from the time when it emerged from the plasma state less than a million years after the Big Bang through the ever-expanding Universe until it bounces into the photographic plate of a telescope or arrives in my retina.
At each point in time and space the Universe has expanded and continues to expand during the travel, so in order to come to the next place which was "only" 1 Gly away (see fig. 1 below and table 1), the photon, heading for the next one Gly of travel, must add the expansion to its travel. And the photon cannot make up for the added distance by speeding up, for it is already traveling at the maximum permissible velocity, that of light in vacuum.
So when the photon reaches us it has not only traveled about 46 Gly during the nearly 14 Gyr of travel but has also itself been "dragged out" by the expansion, and so has its wavelength, pushing it towards the infrared end of the spectrum. Thereby it has lost so much energy that it is a miracle if it ever reaches the Earth in a state where it may be detected.
But could we not have chosen to follow a more potent light pulse? No, our purpose was to learn something about the infant Universe, and we have chosen the absolute shortest route. Had we chosen a more vigorous photon, it would have come from distances closer to us and been unable to tell us about the remote past.
Note that our route (see fig. 1) traces a curve that becomes ever more bent on the way back towards the Big Bang, and if you mirror it below the horizontal bottom line (the Scale axis), it looks like a pear. If furthermore you rotate this pear 180º around the Scale axis, you will have a three-dimensional, virtual pear. This is called our past light cone and is of utmost importance to us. It is our now.
In principle, the surface of the past light cone displays all the information about the Universe that may at any time reach us from the past:
In fig. 2, I have isolated our observable Universe from the rest. Above in the figure the trajectory of a photon is shown from shortly after BB till today. In slice no. 3 a black spot can be seen. This is Supernova 1997ff whose explosion was observed in 1997 with a redshift z = 1.7. The light had then been 10.85 Gyr underway from when the Universe was only 3.15 Gyr old.
Each of the 14 vertical slices represents 1 Gyr of expansion. Imagine how the surface of the entire cone is speckled with billions and billions of infinitesimally small light pulses (as suggested in black on slice no. 6, where the Universe expands from 5 to 6 Gyr). They are quasars, galaxies, galaxy clusters, supernovas, star clusters, shining gas clouds and single stars with their planets.
This ancient light part of which has been en route since the Universe became transparent (see below), i.e. nearly 14 Gyr, reaches us simultaneously with light from the Sun or Moon or from the nearby football stadium emitted just a fraction of a fraction of a second ago. The fact that the electromagnetic waves have been reflected by the mirrors and passed through the magnifying lenses of telescopes doesn't alter the fact that they are here - otherwise they could not have been amplified.
Now, I can almost hear someone saying, 'He insisted just now that it is wrong to imagine that you can watch the Universe from the "outside" as there is no outside the Universe, and now he presents us with a colored, almost 3-dimensional Universe and stresses that it is the past and therefore absolutely non-existing!'. Correct, but with fig. 2 I wanted to give you an idea of what has been going on in our small, observable fraction of the totality we call "the Universe".
The light is here and could present us with an image of the very young Universe, provided we always had ideal observation conditions such as super powerful telescopes, no interfering atmosphere or light-blocking celestial objects and gas clouds in the line of sight, and provided the expansion of the Universe had not weakened the farthest waves by drawing them out to the point where they are hardly discernible.
The lack of transparency in the young Universe, however, presents yet a limitation: During the first several hundred thousand years of expansion the super-high-energy photons collided vigorously with protons (hydrogen nuclei) and electrons so as to prevent them from combining into hydrogen atoms, thus maintaining an opaque plasma state. But once the temperature of the plasma fell below a certain level and thereby the energy of the photons, protons and electrons paired up to form hydrogen in the state of gas. Hydrogen gas is transparent, and suddenly the Universe became transparent, allowing the photons to promulgate across space. But there is no way we can see farther back than to this moment, thus placing yet a limit on our look-back time.
However, our past light cone is not "stationary". It follows the expansion of the Universe, thus moving along our Scale axis (see fig. 1) at the present expansion rate of the Universe, the incredible speed of 28% of the velocity og light, or 83,600 kilometers per second. Simultaneously, each year one light-year is added to the observable Universe as light from far away has had time to reach us. Thereby it successively shows us new celestial objects and later snapshots of those we already know.
Now make the same mental exercise with the arc for the Universe "now" (the outermost arc in fig. 1) as you did with the pear, our past light cone, and you will get a balloon on whose spherical surface the whole Universe "now" is displayed, including our "now" (See fig. 3 below) . If you compare the balloon with the much smaller "pear" - our past light cone - this will give an impression of how vast the unknown and inaccessible part of the "real" Universe is.
Stars move around the center of their parent galaxy. It takes our star about 200 million years to make one circuit of the Milky Way. Galaxies and their clusters move away or towards each other. These are "local" movements and have nothing to do with the general expansion of the Universe.
But on an even larger Scale, super clusters of galaxies are moved away from each other, in my model on the surface of the outer shell (think again of the spots on an expanding balloon), all at the same rate, and driven by the expansion of space which is 28% of the speed of light, but which is today thought to have begun accelerating.
We must bear in mind that the pear - our past light cone - is a two-dimensional analogy to the observable part of a three-dimensional, real Universe. Nowhere do we experience the pear-shape. On the contrary, we perceive ourselves as being at the center of a spherical bubble where all celestial objects apart from the nearest two appear stuck to the inside of the balloon.
It may help to visualize this by imagining that the outermost shell (the 14 Gyr one) is stationary; it has suddenly been halted in its expansion. In such a Universe, all information which gets to us, will come from a flat 'hemisphere' with a radius of 14 Gly, because no light older than the age of the Universe can reach us. But in another million years this radius will have been expanded to 14,001 Gly, thus giving us a million years more information about the rest of the Universe.
Applied to our expanding Universe, the 'cap' curves ever backwards for 14 Gyr towards the Big Bang in a pear-shaped cone. But just as with the imagined static Universe, we at the stalk of the pear (our Now) perceive being in the center of this our pear-shaped, observable Universe. This results in another weird thing about the way we perceive the Universe; the traditional conception is that we are at the center of the inside of a vast, distant sphere with only the Sun, the Moon and perhaps the planets between the sphere and us.
The more contemporary conception is that the further out we look, the larger the Universe becomes, and the older the observed celestial objects. This is of course supported by the fact that as far as we can see with the naked eye (some 2.4 million light-years) the observable Universe actually gets bigger and bigger.
Both conceptions are wrong. Imagine our horizontal pear cut into vertical slices (see fig. 2) with the same age-distance between them, for instance one Gyr. Now we shall be going back in time. We accept that because of the small size of the first slice of the pear (the cone) there must be few objects in the start, only the Moon, a little further out the Sun, the Solar system, the Milky Way, then the Andromeda galaxy etc. The numbers grow steadily as each slice gets larger and the visible Universe grows accordingly.
But gradually this changes as we look further back: From about 5 Gyr ago (when the real Universe was half its present size) the observable Universe begins to shrink and thus the distances between the galactic clusters, but at an even faster rate. Instead of meeting older galaxies we now see younger ones, and further back just stars until they, too, disappear altogether when the Universe was only 100-250 Myr old. This is because not until then did the stars begin to develop, later gathering into galaxies, clusters and finally galactic super clusters.
There is a seeming paradox here: In the beginning of this article I used an infinite number of transparent hemispheres to illustrate that there is really depth in the observable Universe as the distance grows. But as the observable Universe as shown bends back towards the Big Bang, these transparent hemispheres which have so far been stacked each one on top of the other as their size and distance grew, will now become smaller and smaller as they are stacked "on top" of the previous one! It becomes even weirder if one imagines oneself suspended in free space so that transparent, complete spheres surround one.
But where on fig. 2 would our nearest galaxy, M31 (The Andromeda), appear? As slice # 14 "contains" one thousand million years (Myr) of past light, and as light from M31 reaches us from a position only 2.4 Myr away (or some 1/400 of slice # 14), it would appear inside a barely discernible dot at the apex of the pear. This should give you some idea of the immensity of the Universe and of man's insignificance.
Fig. 1 lends itself to other interesting interpretations; let a) be a galaxy, born 12 Gyr ago. We see the galaxy now when it was 3 Gyr old and was located in b), 9 Gyr away (when the Universe was half the size it is now), and when its light was redshifted to z = 1. The galaxy is moving away from us at more than 80% of the speed of light. If one of the stars in the galaxy develops into a supernova and explodes 7.5 Gyr ago when it is 4.5 Gyr old, the light from its explosion will reach "us" in the better part of 2 Gyr, following the dotted line from c) to its intersection (not shown) with the continuation of the Scale axis.
The above-mentioned galaxy may be used to illustrate yet another difficult cosmological concept; an object's Distance Now and Distance Then (DN and DT, see table 1). DT is the distance in Gly between an object at any time in the past and our World Line (the Scale axis, see fig. 1), at the time of the light emission of that object if the Universe had been static at that particular time, so that the light would have propagated along the shell (in my two-dimensional rendition) and not been drawn out by the expansion. Distance Now, DN, is the distance in Gly which the light from the same object, due to the perpetual expansion of the universe, must travel to reach us. This distance is larger than the travel time Gyr. The travel time for light at z = 1 is 9 Gyr, whereas the travel distance is 12,2 Gly. Light which has been almost 14 Gyr on the way has had to travel 46 Gly ! DN is necessarily larger than DT, and the further we go back the difference between them becomes greater.
In fig. 1, DT for the galaxy in b) is exemplified by the enhanced arc between b) and the Scale axis. When the light was emitted from b) (14 - 5 =) 9 Gly ago, "we" were at a distance DT of 6.14 Gly from b), so if the Universe had been static it would have reached us in just 6.14 Gyr. If the galaxy continues to follow the expansion from b) along the expansion radius it will intersect with the outer shell at d) where it is today, several Gly away from us. It will take several billions more years to reach the point where "we" are then. The above argument may be deployed for any other light-emitting object at any time in the past (see table 1).
The extremely important Cosmological Principle has been touched upon earlier. It asserts that each location is equivalent to any other; no observer any place occupies a point of vantage in the Universe. I have attempted to visualize this with the pear-shaped, dashed curve, radiating from the point f) on the outermost shell in fig. 1. An observer in f) will look back in time along the curve whose form is identical to ours (of which only half is shown) but will naturally see an entirely different picture of the Universe from ours. We can observe the object f) now, but what we see is how it looked 5.5 Gyr ago at point e) from where its light reaches us with a redshift of 0.39, and at which time it was moving away from us at 32% of speed of light (see table 1). But the light from f), emitted Now, will not reach "us" for the first several Gyr, depending on whether expansion of the Universe accelerates or decelerates.
Let us return for a moment to fig. 3 ("The universe now"). As already stated, what it suggests: Viewing the universe from the outside, is of course an impossibility: A much more accurate picture would be a dotted circle implying a void and with one diminutive dot inside the circle - our Now. This would better support the fact that we know nothing about and can have no knowledge of what happens anywhere else in cosmos Now. Any acquired knowledge will be as old as the traveling time to us. It will be history, the older the longer it has been en route, and the further back we look the more obsolete it is.
We will never be able to explore even a tiny part of "The universe now". It is a universal, all-encompassing but illusory and unapproachable "now", protected by the velocity of light as the maximum obtainable speed of a message. It is a totally different "now" from the everyday now of astronomers, cosmologists and all the rest of us, the NOW which we pasted on the surface of our past light cone, but which is really “second hand” if anything. Our most up-to-date now is of course the Now on fig. 2 and the "us now" on fig. 3, marked on the apex of the past light cone.
Here I must complicate things somehow; our observable Universe as posited by me is necessarily finite in size and in principle calculable. If the "rest" Universe is also finite in size, then we may know its approximate size and the proportion between "ours" and the "rest". However, if the "rest" Universe, the unapproachable part outside our light cone, is infinite, it follows that "our" (observable) Universe is only an infinitesimal part of the whole.
We all agree that the Sun will go on shining in our lifetimes because our memory, our literature and our scientific studies confirm it, but on the Cosmic Scale we are forced to conclude that the remoter parts of the observable universe do not existent. As we have seen, what exists is the light that reaches us. About the remote universe itself we can only conjecture. But as new light keeps coming in and as the astrophysicists confirm with ever greater precision that the observations follow the same set of basic physical laws, a permanent state of well-deserved expectations is created with regard to future observations; we tend to equate the light we see "with the real thing", and for practical reasons we say that even the most remote galaxies we can observe "exist". We transfer the concept of existence onto something which no longer exists.
This non-existence is easy to grasp in the case of galaxies that emitted
their light billions of years ago. But as the light gets younger and younger,
coming from nearer and nearer celestial objects, we do not hesitate to include
these objects in our existence. The Moon certainly exists: we can see it there,
we can bounce signals off its surface, and we have walked on its surface.
Where, then, is the borderline between the cosmic
and the local, the non-existent and the extant? In principle there is none.
It seems that our concept of space and time lies at the root of these apparent
contradictions. We can never truly understand space and time if we ignore the
trinity of Relativity, Quantum Mechanics and Cosmology. Let us look more closely
at the structure of the universe:
The
Constants of Nature and the Great Theories
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At http://members.fortunecity.com/dlmcn David McNaughton gives his views on Astronomy, Islamic Astronomy and World History.
(The two Japanese/Chinese characters in the background read "uchuu" in Japanese, which means "Universe")
The page has been written by a Non-scientist for Non-scientists with a more than superficial interest in the universe around us, its impact on us and our place in it. Please do not be surprised if the text is different next time you look at it.