Posts Tagged ‘Boltzmann’

Simply put, Olbers’ thought was that if the universe were infinite with stars distributed equally throughout, then such stars would provide an infinite amount of light to shine upon any point in space. Even if dust inhibited some of the light, the sky would be brilliant at all times.

But the sky is dark.

How can that be? How can the universe have an infinite amount of light and yet offer its inhabitants a dark sky?

Ordinarily, the word paradox refers to a pair of statements that seem to contradict, but, upon closer examination, turn out to be unexpectedly compatible. In the case of Olbers’ Paradox, however, something different is going on. Some people are seeing a contradiction and concluding that the universe must not be infinite. Others are so committed to an infinite and eternal universe that they persist in calling it a paradox and trying to find a way that it can work.

History of Olber’s Paradox

Olbers’ paper on this subject dates only from 1823, but though he got his name on the idea, it seems to pre-date him by a good 200 years or more. Thomas Digges, who was the first to discuss Copernicus in English, and whose life falls between the death of Copernicus and the very early teaching career of Galileo, talked about the problem of so much light.

Shortly afterwards, in 1610, Kepler talked about it, and concluded that the universe must be finite.

The first detailed presentation was given by Lord Kelvin in 1901, and he proposed to resolve it by considering that the distance to some of the stars was so great that their light had not reached us. One wonders how such a state of affairs could arise, given that the light has an infinite amount of time for its travels, but of course the lives of individual stars are not infinite, so perhaps the universe proposed by Boltzmann was the right approach for maintaining the idea of a paradox.

A material totality

Still, this takes us back to the question of a genuine material totality.

  • Material objects can be counted.


  • An infinite universe with an even distribution of stars must have an infinite number of stars, which cannot, therefore, be counted.
  • Therefore: there can be no such no such universe.

Boltzmann’s proposal, so far as I read it, did not necessarily present an infinite universe, just one so large that its parts did not interact. I wonder what he thought kept the parts apart?

But Kelvin was really going for infinity, and the reason for this was pantheistic at heart. Remember that if the universe is so segmented that its parts do not interact, then there is nothing scientific to say about any part except our own. Even the assertion that those other parts exist is not scientific. Why would you say it? Only because you find an infinite universe comfortable or because you are uncomfortable with the metaphysical implications of a finite universe. There’s less room for accident.

A matter of philosophy

Still, even if you have unworthy reasons for believing the material universe is infinite, unworthy reasons do not, by themselves, make a proposition wrong. False premises do not make a false conclusion; they make a conclusion with uncertain truth value.

So Jaki goes farther.

He states, as a point of philosophy, that countability is part of being material, and that there cannot be a collective material entity that does not have a countable totality. In other words, he is proposing a philosophical proof for the existence of a finite material totality.

At least this is how I understand his writing.

Note that since we are a part of the universe, it is not really like other scientific or astronomical objects. You can study all stars without taking human life into account  – or all leaves or all bugs or all atoms. But the universe includes us, and its nature must be understood to include the fact of our presence.

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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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