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Posts Tagged ‘Olbers’ Paradox’

God’s image

The universe is in God’s image: it has to be. In what other image could it be made? “Before the universe,” there was nothing, no image to copy, no starting point, no pattern. Serious “nothing” is much emptier than air and space.

Now, the image of God imprinted on the universe does not have the same aspect as the divine image that is imprinted upon us, because we are personal beings, and the universe is not. Let’s think about this a little before going on. When scripture says that we are made in the image of God, it uses a phrase that actually suggests sonship, the way that Adam’s children are in his image. The universe and its elements are not like that, and could not be.

Why not?

Take a minute to recognize that we ourselves could not be persons if our “parts,” – our hands, our feet, or our molecules – were other persons. Who would be in charge? Nor could we be persons if we were part of a planetary person, such as Gaia, because then the freedom to respond to destiny would either be located outside ourselves or else divided with others. That is what personal nature means: the capacity to seek a destiny with one’s whole being. It’s not about free will in the sense of trivial decisions, but about the capacity to seek our inwardly known destiny.

The universe cannot have this personal sense of destiny and still make room for our own. It is not part of God, and we are not part of it. But the universe does reflect the nature of God as the work of any artist reflects his nature and opinions, and for this reason it is always the case that new information about the universe, including new information from the natural sciences, can suggest new perspectives that are of interest to theologians, new ideas about God or deeper insights into his nature. These perspectives are just that, perspectives, not dogmas, and they do not excuse us from examining yet more of the universe. Each perspective has limitations; but each also has a new fund of truth.

But enough of abstractions. Let me give you an example of a perspective that was very quickly offered to counter the concept of an infinite universe which naturally arose in the wake of the Copernican insight that the universe was much, much larger than had been considered.

Olbers’ Paradox

If the universe were infinite, an infinite extension of space filled, or even just sprinkled, with an infinite number of stars, then the starlight converging on any given point of space would be infinite. For the light of an infinite number of stars, however weak, would add up to an infinite amount of light. Therefore the sky would not be black or even dark at any time, day or night.

You are thinking that if the stars were very far away, the light would not be infinite. That is an understandable objection, but it really depends on a sloppy concept of “infinite.” Infinite does not mean “really a lot” or “much more than usual.” It means there is no limit.

Somebody named Olbers pointed this out, and called it a paradox, meaning that he was surprised that these two statements should both be true: that the universe is infinite and that the night sky is dark. Actually, a paradox is only an apparent contradiction; this is a real one, meaning that one of the statements must be false. Since anyone can see that the night sky is dark, the universe must not be infinite.

There is a similar gravity paradox: If the universe had an infinite amount of matter, its gravity would be infinite, and it would disappear in a clap of thunder, or at any rate, a Great Collapse. Well, not even so; it could never break out in a Big Bang if the gravity were infinite. Again, the failure to understand this is the simple failure to understand the difference between “very large” and “infinite.”

One of the ways people try to get around these contradictions is to suggest that: in an infinite universe which is expanding (as ours is) some of the matter will expand so far away that it will move over the horizon of gravity. It will, in terms of relativity, apparently accelerate over the speed of light and its gravity will no longer affect what is left behind. But think about this. Even if gravity goes over such a horizon that it won’t affect you personally, it will affect something halfway between you and the horizon, something that does affect you. How does that work?

The answer is that it would work various ways at various times, and every so often, so much would be pulled together that it could not come apart, and over an infinite time, the Great Collapse would occur, perhaps in stages, but over an infinite time, there would be nothing left.

It could be worse: if the universe is expanding all the time, and if it is of an infinite age (infinite universes are always infinite in time as well as space) all the matter in the universe must already (in its infinite past) been completely scattered so that nothing but a tenuous puff of dust remains. How could there be a planet?

No, no, you say! The universe is constantly being created in the empty places, so its infinity keeps on going.

This is simply hilarious, and again, it is a failure of philosophy, a failure of thought, not of experiment. If the universe is self-generating in all the empty spaces, then there will be an infinite influx of matter coming towards us (towards any given point) from every horizon out there, and we will be crushed. Indeed, we will already have been crushed in the infinite past.

Stop thinking that infinite means “very big” and face it: the infinite is unimaginable. You need to think past your images; you need to use your reason all the way out to the end of the thought.

These two “paradoxes,” these twin impossibilities of infinite light and infinite gravity, were under discussion for hundreds of years, and it was a form of philosophical blindness for people to have gone on thinking the universe infinite. The progress of the natural sciences, which briefly suggested an infinite universe, very quickly turned around to demand a finite universe.

Gravity is not, as the ancients thought, just a condition of earthly things which seek the center of the earth; and light is not just a visually searchable property of celestial beings. Once these two material aspects of the physical universe were better known, once we understood that both gravity and light are law-abiding aspects of the material world and fully subject to mathematical laws, then the habit of assuming the infinity of the universe should have begun to collapse.

Instead, this habit persisted, and this was a religious and philosophical blunder. Indeed, it was a philosophical blunder whose persistence depended on the tenacity of religious unbelief and the consequent determination to avoid anything suggesting creation.

This is not to say that the finity of gravity and light prove the existence of God. We cannot jump from science to philosophy or theology in exactly that way; but the necessary finity of gravity and light do demand respect for the concept of a finite universe and attention to the implications of that finity. In that sense the face of God peers out from the mists of a dawn without a yesterday.

It is hard to be an atheist.

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Gravity

Newton grew up in England, and he went Cambridge University, and right as he was beginning his education, the plague struck, the college closed, and he had to go home.

It is a fact that his mother had an orchard, and it is more than likely that he sat in that orchard, reading some of the books he would have read at school, including a brand new book, just published: Galileo’s last book, translated into English at long last. He read that Galileo believed that the orbit of the Moon was following the very same law of gravity as the fall of a spoon or anything else, such as the apples around him. He worked out the math and – with a little push from his friends – he published it thirty years later

A little push: his first thought was that this knowledge was too sacred for the common man. Robert Boyle and others were aghast. “You must publish,” they said.

“Anyway, it’s too expensive,” he answered.

“I’ll fund it!” exclaimed Boyle. And that is why we have Newton’s thoughts.

Since that publication, we see that it isn’t just a mathematical convenience to locate the Sun in the center of the solar system; rather this location is due to its more substantial mass. Gravity, the most familiar and fundamental of all physical powers, is now understood to govern the orbital motions of the entire solar system. That the Sun was vastly larger than the Earth was already known, and this relationship with gravity was the final disposition of the Ptolemaic system of cycles and epicycles and all the embroideries on it. Geocentrism after Newton amounts to a denial of gravity.

Deepening space

Time moved on. Telescopes improved with the passing of years, and with their improvement, more and more stars appeared. Still no parallax, but with so many stars invisible to the naked eye but visible to telescopes, might it not be that they really were just farther away? The impression of deep space became stronger and stronger.

How deep?

Newton had thought the universe was finite, but where did it end? Bruno’s riddle about his arrow was still unanswered, and the impression of utterly endless spaces was growing.

Yet there were very good reasons for thinking the universe finite.

One became known as Olbers’ Paradox – named for a scientist who lived in the 19th century, but the idea was already around here in the 18th century, 100 years before it got his name. It went like this:

Suppose the universe is infinite, and suppose it is everywhere sprinkled with stars, just as we see – thus with an infinite number of stars. In that case, if you should go into a field at night, the light of an infinite number of stars must fall about you. Only a very small amount of light from each one, but… infinite is infinite. There would be no dark sky in an infinite universe with stars throughout.

There was a similar line of reasoning about gravity: an infinite number of stars would have an infinite gravitational pull and the universe must collapse into its own weight. This was called Bentley’s Paradox. It should be called Bentley’s proof of a finite universe, just as Olbers’ Paradox should be called the light proof of a finite universe, but some people were so convinced that the universe was infinite that they called it a paradox, as if they were dealing with a trick of thought, not with an impossibility.

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I would like to initiate an extended discussion of Stanley Jaki’s book, Is There a Universe?. Jaki had a PhD in physics and also one in theology. His specialization was the history of science, and he wrote a number of illuminating books on the topic of the relationship between faith – a Catholic faith – and science. I remember telling my mother about him, and how she cried, saying if only my father had known him, he would not have felt so alone as a Catholic astronomer.

I have already touched on some of the themes of Jaki’s volume, but now I will take it one step at a time.

The New Science – cosmology

The idea of studying cosmology is new, relative to the history of philosophy, because in the world-view obtaining up to the time of Galileo, it was not clear that the stars or the planets or even the Moon were subject to the same physical laws as the earth. For that reason, the only relevant physics was earthly physics. As it gradually became clear that the planets and even the sun share our physics, and that other stars were suns like ours, there came a time to speak of the universe as a material whole or at least to consider whether it was a material whole. That’s what cosmology really is – the study of the universe as a material whole.

But it was a slow start, because the legacy of infinity as the home of the stars was not quickly shaken, and has been repeatedly resurgent even after it first gave way.

Isaac Newton thought the universe was finite. His dates are 1643  – 1727 and the year of his birth was the same year that Galileo died. The “infinite” mischief came primarily in the following generation.

In 1755, Immanuel Kant argued that the universe must be infinite because it is the work of an infinite God. This quick argument for cosmological infinity is worth addressing, since it has an undeniable intuitive appeal.

First, a word about the possible relationships between just a few objects: Suppose three objects interact. Each one may be aware of itself. Each may be aware of the relationship existing between itself and each of the other two. Each may be aware of the other two and their mutual relationship. Each may be aware of the relationship between the paired others and itself. Each may be aware, from a different perspective, of the relationship of the threesome. Each may be aware of the change in itself due to reflection on each and all of the relationships just listed. Each may participate in changed relationships with each other and with each twosome and with the threesome as a result of those reflections.

Do you see where this is going? A universe with as little as three objects can start pushing into an endlessly complex set of relationships just from that simple starting point and its interactions. In a universe with billions of material objects and also billions of personal beings, you can have a suitable expression of infinite creativity even without an infinite material universe. The relationships can generate an endless network, even if the relational objects are finite in number, and all the more so if God himself is in relationship with the persons in his universe.

That being so, it is arguable, against Kant’s assertion, that an infinite God could please himself in the creation of a finite universe. In saying this, I do not mean to ignore the fact of revelation, which takes precedence over our confused ramblings; but it serves the unity of the human mind to observe, whenever we can, that our theological opinions have also a basis in natural reason.

In 1761, John Heinrich Lambert turned back to finity, stating that the universe had to be finite because there could not be an actually realized, infinite collection of material beings. This did not deter Kant, who was still living, and neither did Olbers’ Paradox nor the similar gravitational paradox described by Bentley – which pointed out that an infinite universe would have intolerable quantities of gravity and light.

In the late 1890’s, Boltzmann stated that the Universe consisted of a whole series of universes, 7 x 10100th light years apart, each with its own physical laws. Since the universe as we now know it is only about 109th light years across, a number such as 7 x 10100th – however easily it slides across the mathematical tongue – is utterly beyond human imagination. I do not know where Boltzmann got his number. Presumably he was trying to have infinity but keep it at a distance where gravity and light would not overwhelm us. His idea is worthy of mention because he was an extremely intelligent and reputable physicist and it sounded so authoritative. The universe would generally – though not universally – be considered infinite from then until 1965.

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