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Cosmology


This book would not be complete without delving into the king of all physics topics: the field of cosmology. Cosmology attempts to account for everything at the large scale and includes the study of the universe and everything in it. It studies questions of its size, structure, its past, and future. Despite the best equipment we have however, little is known about these areas because all our information comes from studying what the universe looks like at the present time from our tiny corner we call the Solar System.

But just because our knowledge is far from complete, that doesn’t mean we shouldn’t try. Hence the focus of this chapter will be to address such questions. It will take the knowledge accumulated in prior chapters and extrapolate it to a large scale. In the process it will generate predictions that are at odds with conventional wisdom. Comparisons will also be drawn with the mainstream view known as Big Bang Cosmology or more commonly as Big Bang Theory (BBT).

 

The Size of the Space

First things first, we need to get a handle on what we’re discussing. The best way to do so is ask: how big is the universe? There are two aspects to this question. The first one concerns the total amount of physical matter and the second concerns the total volume of space surrounding it. We’ll start with the second since it’s easier.

How large is space? Common sense would suggest that it must be infinitely large in all directions. Because even if you could imagine a bubble surrounding all of existence then, no matter how large you make that bubble, there will always be more space on the other side of it. A purist might object to the question, saying that empty space has no physical identity and hence the question is meaningless. That’s true in a sense so I’ll rephrase: if you were to fire a projectile away from Earth in a randomly chosen direction, and assuming this projectile was able to pass through astronomical debris, how far would it go before stopping? The logical answer is that it would never stop and its distance from us would continue to increase without limit. Again this points to an infinite amount of space.

BBT dislikes the idea of infinite space and declares it to be finite by saying it curves back on itself. The analogy made is to compare the universe to the surface of a sphere. The surface of the sphere is finite because its two-dimensional area has been curved back on itself via a third dimension. In a similar manner we might suppose three-dimensional space could be bent within a fourth dimension. If an additional dimension existed then it should be possible to curve 3D space into a 4D ball (whatever that looks like) and make it finite. However there’s a problem. In the case of the 3D ball, its 2D surface is finite but the space surrounding the ball is infinite. In the same way, limiting a three-dimensional space would require an infinite forth-dimension. Alas there appears no way of avoiding infinite spaces.

A second question that goes hand-in-hand with the above concerns time. Does time extend for infinity in both past and future directions? Common sense suggests that time must be infinite because there must always be a time earlier than any historical era and later than any futuristic era. BBT places a limit on the past and says that both time and space came into existence a limited number of years ago (around 13.7 billion of them). It does this by suggesting some type of space-time curvature with time curving back on itself or into a point. How this works is unclear, but it implies a second time dimension must be available in which to bend the first – which means, like the additional space dimension, this time dimension would also be infinite. Now going forward, BBT places no limit on the future and allows it to extend to infinity. Thus BBT does admit to infinite time spans, at least in the forward direction.

 

Size of the Physical Universe

The next question concerns the size of the physical universe. The physical universe refers to everything having physical form. It collectively includes galaxies, stars, planets, nebulae, cosmic dust, gas, subatomic particles, etc.; and excludes the empty region of space surrounding it. To make the question less ambiguous we could ask: is there a finite number of particles (limited mass) in the universe or an infinite number (unlimited total mass)? I will argue that the universe contains a limited total mass confined within a limited region.

 

Olbers’ Paradox

The first support for this argument has to do with something known as Olbers’ Paradox (named after astronomer Heinrich Olbers). It may be phrased like this: if there were an infinite number of stars then the night sky would be awash with visible light because any line of sight would ultimately terminate on the surface of a star. Yet instead most of the sky appears dark. Solutions to this paradox are generally two fold. The first suggests that the number of stars in the universe is finite. The second suggests that the universe is of limited age and the light from distant stars hasn’t yet reached us. BBT includes both these ideas, although in a different form.

The second of these is the least plausible. It states there are an infinite number of stars but they only got ‘turned on’ a finite time ago. The problem with it is this ‘turning on’ process could only be a one-time event because even if we could turn the stars off again, the sky could never become dark since light from ever-further stars would forever continue reaching us. A once-off event within an infinity of time becomes a problem for probability reasons; as will be explained later.

 

Infinite Gravity?

The second support for a finite universe has to do with gravity. Consider this question: how much gravity would there be on an infinitely large planet? To answer, start by considering a planet with finite radius and uniform density. We know that gravitational acceleration is inversely proportional to radius-squared, so this would decrease the surface gravity as its radius increased. Except gravity is also proportional to mass, which is proportional to density and radius-cubed (volume). Dividing radius-cubed by radius-squared then, tells us that overall gravity will be directly proportional to radius. Thus as the radius of this planet heads to infinity, so too does its surface gravity.

Next question: what will be the gravity of an infinitely sized cube of finite density? Since a cube can contain a sphere of the same diameter, we know that such a cube must also have infinite surface gravity. We also know this gravity will be infinite no matter how low the density.

Now here’s where it gets interesting. If you divide the universe into two imaginary halves right at where you’re sitting, then each half will represent the face of an infinite cube. Therefore, if the universe was physically infinite, you would experience an infinite gravitational force in each direction because the average density in both ‘cubes’ is non-zero.

Will this be a problem – being surrounded by infinite gravity, and immersed in an infinite amount of gravitational field? Some may say no, because the infinite forces come from opposing directions and the fields would cancel to zero.

On that point they may well be correct. However this is just a precursor to a more important argument that I will present now.

Return to Olbers’ Paradox. We’ll suppose the universe consisted of an infinite number of stars, each having the same brightness as our Sun. Here, both the day and night sky would be uniformly bright as our Sun, and like that in all directions. Despite it being so close, our Sun would appear no brighter than any other part of the sky.

Now consider the gravity situation on Earth. If the universe contained an infinite amount of mass, gravity would be the same in all directions. Because there would be as much mass above your head as there would be beneath your feet. Therefore the gravity of Earth would have no effect on you. Despite it being so close, its field would be no stronger than the infinite field surrounding you from all directions. We would all float off into space.

This again appears to indicate the universe contains a finite amount of mass.

 

Steady State or Evolving?

Another cosmological question regards the behaviour of our universe over long time periods. There are two basic views. The first is the ‘steady state’ view: that the way the universe is now is basically the way it has always been. The second is that it is progressively changing and no longer resembles what it was in the past and will not resemble the future. This is the ‘evolving’ model.

The steady state model allows for variations over time but only those of a cyclical nature, such that an average taken over a long period looks like the average of any period. An analogy would be the water levels of ocean tides: it changes daily but averages-out over the long term. The steady state model extends to infinity in both time directions – it has no beginning or end.

The evolving model allows for cyclical patterns but only within a framework of continuous progress. An analogy would be a stock market index that fluctuates over the short term but heads steadily higher over longer periods. The BBT fits this model and describes an ever-increasing expansion.

Which of these models is feasible? Both have advantages and problems. In the steady state model, its big advantage is that it solves the finite-time problem. It extends forever into both future and past. We don’t need to puzzle about what caused it to begin or what ultimately will happen to it at the end because it has no start or end. But the model does have problems, for example, the stars will ultimately radiate their energy into the surrounding space and fuse their gases into heavier elements. At this point they will be finished because we know of no mechanism that can reverse this energy loss or fusion process. They cannot glow forever.

A second problem has to do with stability, which has to do with keeping astronomical objects at a more-or-less fixed distance. Within the Solar System objects such as planets and moons are attracted to each other via the force of gravity. If they were motionless, this force would cause them to move toward each other and the Solar System would collapse into the Sun. However since they are moving, they are able to keep their distance: centrifugal force cancels-out gravity and the system becomes stable. A similar process occurs in spiral galaxies, where stars can orbit a collective centre of mass. Well that may be fine for individual galaxies but what about galaxy clusters, groups of such clusters, and so forth on ever larger scales – do they also orbit one another to maintain stability? As far as we know, they don’t.

Here’s the problem: if there exists a weak attractive force (such as gravity) between objects then, no matter how weak that force is, given an infinite amount of time it will draw all objects together. Conversely, if there was a weak repulsive force it would push them infinitely far apart. Actually this would be a problem even if there were no forces. If objects are moving in different directions and have no force to stop them then they will eventually drift infinitely far apart and would have done so already. The above statements, of course, exclude localized systems held stable by centrifugal force such as spiral galaxies.

A solution to the above it seems would be to make the physical universe infinite. This would solve the problem of energy loss as all stellar radiation would be eventually captured by another object, creating in a sense a closed system. It would also solve the problem of drift since no matter how far objects travel, the universe will never lose its average density because other drifting objects will replace them. But it won’t solve the Olbers’ Paradox since the sky will again be covered in visible radiation. Nor will is explain how heavier elements such as carbon can reverse their synthesis back to helium and hydrogen. It will also create a gravity problem because objects cannot be evenly spaced and will experience a stronger gravitational force in a certain direction. This will lead to clumping, first by small objects into larger ones, then larger ones clumping with others, etc., all without limit. Obviously this will be a problem if allowed to continue for an infinite amount of time.

Evolving models on the other hand would appear to solve these issues, or at least some of them. For example the BBT describes a finite amount of substance moving outward for a limited time. The finite substance accounts for Olbers’ query and limits total gravity. The outward movement accounts for why the universe hasn’t collapsed on itself (due to gravity) and also how the objects got to where they are currently. And the limited time span accounts for why stars are still shining.

Despite the benefits however, evolving models have obvious drawbacks. In the case of BBT, it is the question of what happened prior to the Big Bang. BBT effectively extinguishes the laws of physics by saying that something came from nothing and without prior cause. Putting aside the implausibility of producing matter from a vacuum, the main problem is the lack of prior cause, i.e. of causality. In any physical process, every event that occurs is preceded by an event that caused the later one to happen. This is true even if the ‘event’ is an object standing still: prior to a point during which it is standing still, the object will be standing at the same location, i.e. the object can’t just appear at that location.

BBT attempts to resolve the causality problem by saying that time also began at that point, perhaps because time curved back on itself at that juncture. However this does little to help our understanding of the question and implies something far more nonsensical than any steady state model. But assuming that these initial problems of matter creation and causality could be resolved, there is another problem that can be phrased in terms of probability.

 

A Paradox of Probability

Imagine there was a weekly lottery that paid a prize to a single lucky winner on every draw. The prize was a million dollars but the odds of winning were a million to one against. Now suppose you bought only one ticket per year. The odds of winning in your lifetime would be quite unlikely. But suppose you lived a very, very long time, like a million years. You would have about as much chance of winning as not – in fact a 63% likelihood of winning at least once. If you lived 10 million years though, the odds of winning would increase dramatically to 99.995%. Put a better way, the probability of not winning a prize during that time would be 1 in 22 thousand.

Now to lower the odds. In this scenario you will buy 10 tickets for the first 10 weeks of every year. What are the odds of winning the prize on all 10 draws? Phenomenally low obviously! The probability of doing so in any one year will be 1 in 10 to the power of 60. But again if you lived long enough you would eventually win. And if you lived much longer again the odds would begin to stack heavily in your favour, such that you should not only win, but win a large number of times.

Now take this to the extreme; say you live an infinite number of years. And let’s say your goal was to win every lottery of every week 1000 years in a row. The odds of doing so are unimaginably small. Yet in your infinite lifespan, not only would you win, you would do so an infinite number of times.

So here’s the paradox. Think of the Big Bang as an event. If it occurred it must have a non-zero probability of doing do. Therefore, no matter how low that probability, given an infinite amount of time it must reoccur and must do so an infinite number of times. If an event occurs only once during an infinite time-span then the calculated probability of it happening is zero and therefore it should not have occurred at all. Thus either the Big Bang didn’t happen or it is a reoccurring event that has happened countless times before and will continue to do so.

Now some may argue this reasoning is spurious because in reality all events are unique, in that they can never occur identically; just as no two people can ever the same. Yes this is true but what we are talking about is the general nature of an event, rather than the way it unfolded at a particular point in history. For example the pattern in which snowflakes form is said to be rather unique but the formation of snowflakes is extremely common. So if a Big Bang can occur, a variation of it should reoccur and should have done so infinitely many times already. Problem is, BBT describes no mechanism by which it could have occurred in the first place let alone how it might repeat itself after the universe has already formed.

So what mechanism could account for the universe as we see it now, particularly a finite universe surrounded by infinite-sized space and preceded by an eternity of time? I will discuss this in awhile but first need to clear up some ‘cosmological nonsense’.

 

Microwave Backgrounds and Dark Matter

In 1964 an interesting discovery was made about our sky. Coming to us from every direction is a low level of radiation in the microwave spectrum. It has a frequency of 160 Gigahertz and corresponds to a blackbody radiation temperature of 2.73 degrees Kelvin, i.e. 2.73 degrees above absolute zero. This is called the Cosmic Microwave Background (CMB). The accepted mainstream explanation for it is that it is radiation left behind by the Big Bang expansion early in our universe.

But that explanation is nonsensical. If an event early in our universe generated a large amount of radiation, that radiation would immediately dissipate outward, thinning as it went, never to be seen again. It would not be ‘left behind’ for us to observe today. When a source of radiation disappears, its radiation disappears with it. The only way for us to see the CMB today would be that it is being generated in our present era. Furthermore the fact that it is coming to us from all directions means the source for it must be something that surrounds us. This rules out a point source such as a ‘big bang’.

In the 1896 astronomer Charles Guillaume tried to determine the amount of energy coming to us from stars. He calculated that the temperature in deep space was 5.6K. That is, if you were within the galaxy, between stars, but not close to any star, you would ‘heat up’ to a temperature of 5.6 degrees above absolute zero (not particularly warm!). In 1926 Arthur Eddington refined this number to 3.2K. In 1933 Eric Regener made another calculation of 2.8K. Now keep in mind all this happened long before the CMB was known and BBT was conceived. What a coincidence then that the CMB should have a temperature of almost precisely that amount. Based on this it seems more likely that the CMB is blackbody radiation coming from the heating of a thin background of gas that pervades our galaxy.

Another mystery relates to our galaxy’s movement. In 1932 astronomer Jan Oort studied the movement of the Milky Way and tried to determine its mass based on the speed that it was rotating – his idea being that its outward centrifugal force must balance its inward gravitational force. What he discovered was that there didn’t appear to be enough mass to generate the gravity needed to hold it together at the speed it was rotating, meaning that the galaxy should come flying apart. The calculated amount of mass required was twice as much as would be contained in the visible stars. To solve this he concluded much of the galaxy was made up of material that was not emitting or not reflecting light. He termed this ‘Dark Matter’.

Initially Dark Matter (DM) referred to objects such as planets, moons, and asteroids. However it was quickly realised that such things would be insufficient to account for the missing matter because those within our Solar System amount to only a tiny fraction of the Sun’s mass. Thus DM was assigned a category of its own and said to consist of particles unlike any seen on Earth. It neither absorbs nor emits light and its only property is to emit a gravitational field, making it undetectable by other means.

Given the above information on the CMB however, it would be more logical to suggest this missing matter is merely loose gas floating about within the Milky Way. If this were the case it would require half our galaxy’s mass to consist of gas (with the rest mostly as stars). Is that possible? A rough calculation shows that, if this gas were hydrogen molecules, we would require one molecule per cubic centimetre to match the mass of stars. This is extremely light – the best pumped vacuums on Earth typically have a 0.1 millimetre spacing between atoms, making them a million times denser than what is described here. Now as to why this gas doesn’t condense into new stars is another question, perhaps it is constantly disturbed by stellar winds. Nonetheless, the presence of such gas would nicely account for both the CMB and DM.


Continued in part 2.

 

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Copyright 2010 Bernard Burchell, all rights reserved.