Cosmic Concerns - Theories of CosmologyCosmic Concerns - Theories of Cosmology

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Cosmic Concerns - Theories of CosmologyCosmic Concerns - Theories of Cosmology

LIVING IN A FLAT UNIVERSE

The news is out. We live in a Flat Universe. What does that mean beside suggesting space is Euclidian and not other Riemannian forms being contorted on the large scale? In a way its like a 'Flat Earth' but a good deal more exciting because it is still framed in a Hubble expansion and a Big bang paradigm. But being 'flat' means it is more comprehensible, being restrained to many linear features or more specifically 'linear as far as the eye can see'. Yet, things are far from sitting still, objects evolve and space expands. While the latter is indeed mysterious, the new linearity allows certain comparisons we will explore here.

The Hubble un-Constant

The Hubble Constant is derived from the red-shift of light of distant galaxies and the basis of an expanding Universe and more specifically the Big bang paradigm. But it's not a constant. I don't mean that its value hasn't been modified based on better observational data this past half century when the idea was first discovered and formulated. But no, it is more like a rate, an apparent recessional velocity of distant galaxies per unit of observational distance. Underneath is a more pertinent factor. Its value changes with the age of the Universe and at half its age, was twice as much. When we think of a Universe some 15 Billion years old (Byrs old), your not going to hear about any annual change as being relevant to us, but when you recently heard "The Universe is flat and will expand forever at an accelerating rate" (Flat Universe Revealed, Astronomy Aug. 2000) a little more explanation is in order. What does 'flat space' mean in terms of the Hubble expansion picture, its principal basis?

Starting closer to home or at least some other troubled spot elsewhere on the globe with an exploding hand grenade - eg. pieces of shrapnel all flying off in different directions at different speeds. Let's say our observer is a pretty hardy ant on one fragment looking at the other fragments, leading a fast life with all the modern toys of determination in his fleeting universe. A variety of reasons give the fragments different velocities, that's not relevant and here we will show simple speeds at a one second reference and make a comparison. In the diagram below, the solid lines are the travel path for the first second, the dashed lines for the next (doubled) second.

The first thing that can be ascertained from this, is that the receding velocity of the fragments from any other fragment remains constant and proportional to the distance apart - totally analogous to the receding galaxy recession relationship. A little more subtle, is that any observer can consider himself at the center of this expansion and that if time were reversed, all fragments would be at the location of the bang itself - this is the essence of the Big Bang and what makes the comparison to this mundane example particularly worthwhile.

The concept of 'where is the center' is arbitrary. This bang might have a location within distant fixed walls that would help make the determination of the true center of the explosion or even if the grenade had some original velocity. In the Big bang, there is no such reference except saying we are at the center of what we observe, but with high precision, there appears a slight frequency difference in the distant Background radiation to suggest we have some absolute motion with respect to the whole - eg. We are going around the sun, the sun is going around the galaxy, etc.

What is the technical meaning of a 'flat Universe'? For a few decades, cosmologists have been looking for evidence of change in this velocity-distance relationship or a ‘closure’ concept associated with mass and gravity and the long term fate of the Universe. Well in this case, ‘flat’ means there is no observable deviation from our mundane example and that the Universe does appear to have all objects together at the Big bang from the farthest observational example.

Before we try to interpret further, let's establish what kind of constant Hubble isn't. If we judge the Big bang Universe to be 15 Byrs old, the constant is 20 km/second per 1 Million light years (Mlyrs). For example, Andromeda at 2 Mlyrs distance would be receding at 40 km/second. But Andromeda has always been sailing away from us at 40 km/sec and 7 1/2 Byrs ago when one million light years away, it was at the Hubble reference distance and value then, ergo, 40 km/sec per Mlyrs and 15 Byrs ago it was at our front door (so to speak). Therefore the constant changes over time. So how can it be tied down? A more extreme example is that our Background radiation, at the limits of red-shift and apparent distance, (and if it were an object) would appear to be traveling away at the velocity of light. Therefore, to get back to time zero requires 20 km/sec x 15 Blyrs/Mlyrs = 300,000 km per second or the velocity of light (Voc). So in a general formula, the Hubble constant at any other time of interest, is really the Hubble Variable = Voc/Mu, the velocity of light divided by the age of the Universe in millions of years. (Recession velocities, often referred to in units Km/sec per million parsec, a difference of 3.26, it will be seen here as per million light years which is more useful to the discussion here.)

So what is meant by 'expanding forever at an accelerating rate'? Other than not readily clear, it deviates from what our mundane example demonstrates - whatever velocity any object has with respect to another, it does not remain the same forever, yet not change the essential element of everything being together at time zero. So before we conclude what accelerating expansion might truly mean, let's continue the linear example and see what other principles can be determined first. Then in the later section ‘True age of the Universe’, return to possible perturbations from the linear model where theory on very distant space differs from our mostly linear Hubble data.

A Cosmologic Feynman Diagram

The well known Feynman world-line Diagram is usually thought of in terms of the micro-world of particle interactions. Its simplicity is in reducing events to their theoretical and observational basics with a strict cause and effect. A major feature is one dimension of space and one of time centered at the event. While scales might vary, here in Fig. 2, time and space are drawn equally, 1 sec = 1 light-second distance and the Velocity of light (Voc) and path of travel is projected at 45 degrees and the event of interest is ‘here and now’. This is shown below, labeled with what appears as trivial and obvious notation, with space horizontal and times arrow from below to above, again centered on ‘here and now’. The Voc cone defines what can be within the limits of cause and effect and the outer limit of radiation information. Depicted is two galaxies in collision and one Sidneyia, to be discussed further in terms of what constitutes 'now'.

Fig. 3 is what may be called the Cosmologic Feynman Diagram, with the principle modification of the expansion of space in a linear Hubble relationship. In addition time still flows uniformly and the Voc is constant over time. There is an origin at the Big bang with an extended space at 'now' and light takes a curved path from some 'then and there'. Conveniently in Fig. 3 the Universe is considered 15 Billion years old (15 Bu) and objects take on a variety of velocities with respect to Voc. What can I say? "Honest, Officer, I wasn't exceeding the Voc speed limit. From where you saw me, it was the road that was expanding excessively."

Cosmologic Views

We've come a long way from imagining what nebulosities might be. The Hubble expansion and consequent Big bang paradigm has powerful explanatory detail however we are still bound by a limited observation range. It is not easy to determine what some distant object is and conversely how distant that object might be. Even with some extreme red-shifts and consequently extreme earlier times, most data is linear with distance. Only our imagination exceeds it into probable physical theory vs actual reality. This continues the hand grenade principle mechanics and outside relativistic effects. Actually, high ballistic velocities need relativistic treatment, space expansion velocities do not.

Independent of the linear range of the Big bang paradigm, three viewpoints can be considered. In one sense, giving 'ourselves' an all time immortality from time zero but still ensconced in our present 'now', what can we surmise concerning what's in our Universe to the farthest reaches in terms of 'objects':

1) In our 'Apparent view' objects are and will stay in our perpetual view at a constant recessional velocity over time. This Universe grows at the velocity of light and now 16 Billion light years large.

2) In our 'Where they were' view, when an objects light started its voyage toward us, at first farther and farther out but ultimately closing back in to the Big bang event.

3) In the 'Where are they now' view, they have all left our observation field of view and as we knew them, doubling their distance from us with each doubling age, independent of the velocity of light.

The large diagram in Fig. 4 Life in a Flat Universe, is busy but reveals considerable insight into the three cosmologic views we may hold but still abide in ‘our’ restrained Feynman diagram.

The space and time scales are equal (1 light-sec = 1 sec) and linear with distance horizontally and time vertically. As we look back in time and distance it's not strange that we would see many different things.

Therefore as astronomic objects tend to vary with the distance-time of the Universe, we can use different representative names. The first chore, while not necessarily simple, is identifying what an object might be, and is discussed no further here other than related to its recessional velocity as measured by its 'Z' number. The objects 'Z' number, a ratio of wavelength observed to a reference here on earth, is the basis of what we know and judge the distance of the object to be in addition to its recessional velocity. An object separating from us by space expansion at 1/2 Voc reduces the frequency of emission (eg. a Lyman hydrogen line) by one half. Real observational data becomes flaky if Z is much above 5 and other factors such as ballistic velocities or gravitational wells come into play. While in the table, the Hypothetical object, if it existed, might be imagined to have a Z number of 15, it could not be measured. However there is an exception, a Z number could be assigned to the Background radiation as a ratio of its blackbody wavelengths. Established at a Universe age of about 0.3 Myrs and with the ‘decoupling’ temperature over 3000^{o }Kelvin compared to 2,7^{o} now, Z would be greater than 1000 and our maximum observable recession measurement. Thinking of this event as an object (something that emitted radiation toward us), its recessional velocity is close to the speed of light.

As noted earlier the Hubble Variable was expressed in terms of the age of the Universe. A proper dimensional equation would be: Hubble Variable = Voc/Ru, the velocity of light divided by the radius of 'our' visible Universe in Mlyrs. In the one case, the age is the time back from 'now' to the Big bang and derived from the reverse expansion rate and applicable to any conceived size of the Universe. In the later case, the 'radius' equation is derived from the extreme red-shift of 'our' Background radiation and hence needs the 'our' qualifier. Otherwise they are interchangeable.

Where objects 'appear to be' and 'where they were' can be discussed together to compare their similarities and differences, recognizing first, we can only know of them within our Cosmologic Feynman Diagram as received distant radiation, which is the only reality and the other views arbitrary conjectures: one not having an absolute preference over the other. But tracing back from the Voc line is the 'Locus of light path travel' and common to all observations - the messenger is light and like any one-days-mail, coming from everywhere at different times but arrives simultaneously. Hence as shown here in one dimension, all must follow the same common path. The path is drawn in Euler segments (rather than a fine integral) to simplify the interpretations.

The latest segment, about 8 Blyrs or half the age of the Universe is mostly linear in time-distance relationships. As noted Andromeda galaxy is 2 Mlyrs away and its image 2 Myrs old. Other 'local' objects a few Blyrs away have their images correspondingly a few Byrs old, but these images are the foundation of the Hubble expansion as determined by their recessional velocities and now declared pretty linear. This yields the 'Apparent' and 'Where they were' positions in a straight forward manor as just, plus or minus the Hubble recession velocity.

The next earlier segment is drawn vertically - light the messenger, pretty much holding its own in the expansion - and where 'Apparent' and 'Where they were' really part company. For example the Radio galaxy at 4 Bu, appears at 12 Blyr (the sum of 8 + 4 Blyrs) away but was only (only!) 8 Blyr away at that time.

In the older segments, the 'light messenger' seems to be loosing ground and each successive observation is nearer the limits of red-shift determination. 'Where things were' are in effect closer to the Big bang origin and while far from our 'now' is closer to our 'here' as the Big bang paradigm would have it. See the table of 'Identified objects' for their Expansion velocity, Apparent velocity, Apparent distance and their 'Where they were' distance. Expansion and Apparent velocities are expressed relative to the Voc. In general, it can be noted that these velocities remain constant over time and while Expansion velocities may be greater or less than Voc, Apparent velocities are always less. Here they are based on there Apparent age divided by the Age of the Universe which of course can’t be greater than Voc. Regardless, all objects are and always will be in our view. As an extra note, the light path trace could be drawn for any Universe age - imagine one intersecting our Cosmologic Feynman Diagram at 20 Bu, 4 Byrs from now. But it would sill dovetail closely with the earlier trace near the Big bang origin.

While Apparent distance is the integral of travel time back to the age the light started its travel and 'appears' in the far distance, the 'Where it was' distance has a maximum of about 8 Blyrs but closes back to the Big bang origin. For example, the Quasar has an apparent distance of 14 Blyrs but was only 6 Blyrs away when its radiation left.

The third view 'Where the objects are now' are on the horizontal 'now everywhere' line. Here we can identify the size of 'our' Universe at 16 Blyrs radius and intersecting the Voc line, separating all the 'local' objects that might be considered in our Universe from those out of it and how big 'our' Universe was back in time. So too, we can delineate another whole universe for the Radio galaxy between the edge of 'ours' and the most distant Quasar at this time, also with a radius of 16 Blyrs. But of course we have no knowledge of these objects now or similarly 'before or after' anything not on our 'Path of light' trace, consequently overall, that's a lot of unknown universe. Yet without apology and in a strict sense, think of our universe as only that curved inextricable trace of light thru space over time, a mere taste of the whole.

Reckoning data and techniques

Along the right edge of Fig. 4 is what might be described as our reckoning data for different ages of the Universe. As noted the Hubble value and 'Z' value is the observational foundation of the diagram and the basis of the Big bang origin. While graphically obvious in the diagram, one other number might be considered useful in establishing and extending the knowledge of the objects and respective viewpoints. ‘D’ numbers or reverse doublings of time of the age of the Universe permits such calculations . While any age universe would be applicable, the 16 Byr old is quite convenient to the technique. For example the Hypothetical object at 1 Bu, is 4 doublings ago. Hypothetical indeed. It might have a Z number of 15. But how do 'D' numbers compare to 'Z' numbers and how can they be used?

While 'Z' numbers are derived from actual measurements and are observationally precise, they suggest both distance and an earlier time thru the Hubble and Big bang relationship, yet must be used with caution in such extrapolations. Astronomers often use the term 'lookback' time or distance to hedge the interpretation. There is also physical limitations in their range. 'D' numbers are mathematically precise subdivisions (successive half-ings) of the age of the Universe - whatever it is - and applicable to the same Hubble or Big bang relationship without range limitations. There are about 59 such doublings (the reverse of half-ings) of time since the Universe was one second old. Still for any range Z = 2^{D} - 1. To create Fig. 4, the following methods are used for each object in an expanding universe

Using the Apparent age to establish when light left its source, 'Where it was' is so calculated: 'Take the distance light can travel in its original doubling period times the number of doublings to the present' (for the Hypothetical object, 1 Blyrs x 4 = 4 Blyrs). This is based on the principle that within each successive doubling period to the present, light has twice the time to cover twice the distance, it therefore travels an equal fractional segment of the original distance during each doubling period over the course of the trip. 'Where it is now' is 'Where it was' and doubling the distance for each doubling period forward? (4 Blyrs x 2 x 2 x 2 x 2 = 64 Blyrs).

Red-shift and Cosmology

On the larger scale of things, us, the earth, the solar system and the Universe are evolving in space and time. Within this dynamism we harbor two related constants: the flow of time and the velocity of light . Yet as constants, both are recognized to be conditionally variable. Furthermore, there is no modern cosmology without observation of the red-shift of E-H radiation from atomic spectra. Thinking about it, and expressed as 'Z' numbers, it is a conceptual wonder; the ratio of specific atomic emissions in distant space to their microscopic counterpart in an earth laboratory. The comparative distance apart is not the first order significance but rather 'why' the comparative frequencies are not the same. This apparent difference has two fundamental reasons and maybe three or more combinatorial reasons. The first I'll call Bio-rates of the source and the recipient. The second is any modification of the wavelength in travel. The multiple conditions occur because a 'Z' number cannot be interpreted without considering collectively the generation, transmission and receipt of the ratio components. And herein lay the details of our cosmic views.

The first, Bio-rate is an appropriate term; the observer and his lab spectra is the reference. Whether on earth or some imagined environment, as far as known, the observers heart rate (so to speak) compared to the atomic spectra would be congruent. Yet the variance of the spectral constant downward is demonstrated in a gravitational well, so we must assume that of the observer too if he were there, reminding us of a major contingency of the source. Simple ballistic velocity or true Doppler effect is the second which modifies the transmission wavelength. The third or fourth on the wavelength may be the cosmic expansion of space over time or relativistic effects on the source velocity, The fifth over them all, is the unknown as to whether the bio-rate or the velocity of light is constant in space over time. We might ask if all other phenomena are truly inert to expanding space.

All of these are inextricably linked to cosmic-lookback, that thin thread to the past. Yet while there is every reason to potentially recognize these different possibilities, a standard cosmological model might display only one, as in Fig. 4, and try to explain all the others as perturbations from this reference. For myself and I think the public, one super equation with all the variables doesn't cut it in trying to explain things.

Variations in the age of the Universe

The true age of the Universe is hard to pin down, but in essence it is that determined by the linear Hubble relationship modified by the various cosmologic models that go beyond observational limits and which tend to reduce that age typically by a 1/3 assuming certain gravitational effects over the duration. (If the Hubble constant yields 15 Byrs, it is reduced to 10 Byrs). The startling example of 1A Supernovas as standard candles at great distance contradicts this theoretical image of the expansion slowing down. How can it be explained?

The diagram in the margin with distance vertically and time to the past horizontally shows three possible Hubble galaxy recession curves.

At 45^{o} is the linear Hubble relationship. Above and below that is a projection for a decelerating universe and accelerating universe respectively. If the True age of the universe line were to intersect the linear Hubble line at 15 Byr, the decelerating universe curved line would intersect earlier (eg. be younger) and the accelerating universe curved line later (eg. taking more time early on).

The confusion comes in when the cosmologic model already assumed the decelerating universe as a gravitational effect and the new data suggests it is accelerating. To what extent? Accelerating to the degree of meeting the linear Hubble value again or even more so? I haven’t heard. Of course we have assumed in all this, that time and Voc are invariant and space expands. Dark energy is now consistent a factor in the changing expansion rate. They all may be up for grabs as we take a 'Deeper look at the Night sky'.

Philosophic views

As in a discussion of the fate of poor Schrodinger's cat, there is a number of views - maybe some contrary within or with scientific consensus. This can be constructive if so recognized. As acknowledged the basic Feynman diagram is all we really have so how can we extend our understanding to elsewhere? The whole of Fig. 4 can be considered a space-time continuum in the Relativity Theory sense even though relativistic effects are not present.

Still there is another way to interpret space and time - refer back to Fig. 2, the basic Feynman diagram. Within the incoming view is two colliding galaxies, say 540 Mlyrs distant. While the whole image is some former 'now', as far as a collision event, we can see a before, now and after. Since stars seldom collide but fine interstellar dust does, we see a region rich in dust pre-collision, a highlighted collision zone in vaporization 'now' and a zone swept free of dust after the collision. The point being, 'now' is the dramatic place change occurs, which this image emphasizes.

Can there be any real meaning to other 'nows' and more specifically, a horizontal 'now' line? Consider first a vertical 'here' line. It so happens that 540 Myrs ago another catastrophic event occurred on a muddy shelf in a shallow sea, collapsing and instantly entombing some ancient critters into what is now known as the Burgess Shale fauna. (Sidneyia is one such critter.) Of course geologists have their way of dating things and judging what the event was, that's not the point but rather again, a special 'now' is created because of change and this is how that 'now' then and there can be projected on the vertical to the here, 'here'. The galaxy collision event is preserved (brought here) by radiation thru time. The Burgess event residuals perpetually reside here but their significance was only recently discovered (by Charles Walcott, 100 years ago). As such, I personally prefer to think of time as the singularity 'now', more a stress-strain of space, like a slippery slope inducing the only way change can occur and therefore simultaneous everywhere on the horizontal line. (Hence simultaneous by definition, not observational argument.) Yet it is arbitrarily interchangeable with the space-time continuum concept, with the major beneficial addition of times 'arrow'.

And finally along this philosophic bent, because the Universe is flat, and as depicted in the hand grenade principle in Fig. 1, if the Voc were not constant over time, or if object velocities were possibly ballistic or proportional in some combination, we might have no way to differentiate it, although we could indeed draw a different Fig. 4 that represented it. Would you like to see one?

Cosmic Concerns - Theories of CosmologyCosmic Concerns - Theories of Cosmology