Tag Archives: cosmic heat death

Boltzmann’s brain

Ludwig Boltzmann developed a statistical explanation of the second law of thermodynamics by defining entropy as being proportional to the logarithm of the number ways in which we can arrange a system [see ‘Entropy on the brain‘ on November 29th 2017].  The mathematical expression of this definition is engraved on his head-stone.  The second law states that the entropy of the universe is always increasing and Boltzmann argued it implies that the universe must have been created in a very low entropy state.  Four decades earlier, in 1854, William Thomson concluded the dissipation of heat arising from the second law would lead to the ‘death’ of the universe [see ‘Cosmic heat death‘ on February 18th, 2015] while the big bang theory for the creation of the universe evolved about twenty years after Boltzmann’s death.  The probability of a very low entropy state required to bring the universe into existance is very small because it implies random fluctuations in energy and matter leading to a highly ordered state.  One analogy would be the probability of dead leaves floating on the surface of a pond arranging themselves to spell your name.  It is easy to think of fluctuations that are more likely to occur, involving smaller systems, such as one that would bring only our solar system into existence, or progressively more likely, only our planet, only the room in which you are sitting reading this blog, or only your brain.  The last would imply that everything is in your imagination and ultimately that is why Boltzmann’s argument is not widely accepted although we do not have a good explanation for the apparent low entropy state at the start of the universe.  Jean-Paul Sartre wrote in his book Nausea ‘I exist because I think…and I cannot stop myself from thinking.  At this very moment – it’s frightful – if I exist, it is because I am horrified at existing.’  Perhaps most people would find horrifying the logical extension of Boltzmann’s arguments about the start of the universe to everything only existing in our mind.  Boltzmann’s work on statistical mechanics and the second law of thermodynamics is widely accepted and support the case for him being genius; however, his work raised more questions than answers and was widely criticised during his lifetime which led to him taking his own life in 1906.

Sources:

Paul Sen, Einstein’s fridge: the science of fire, ice and the universe.  London: Harper Collins, 2021.

Jean-Paul Sartre, Nausea.  London: Penguin Modern Classics, 2000.

Everything is in flux but it’s not always been recognised

Decorative photograph or ruins of Fountains Abbey next to River SkellI am teaching thermodynamics to first year undergraduate students at the moment and in most previous years this experience has stimulated me to blog about thermodynamics [for example: ‘Isolated systems in nature?’ on February 12th, 2020].  However, this year I am more than half-way through the module and this is the first post on the topic.  Perhaps that is an impact of teaching on-line via live broadcasts rather than the performance involved in lecturing to hundreds of students in a lecture theatre.  Last week I introduced the second law of thermodynamics and explained its origins in efforts to improve the efficiency of steam engines by 19th century engineers and physicists, including Rudolf Clausius (1822 – 1888), William Thomson (1827 – 1907) and Ludwig Boltzmann (1844 – 1906).  The second law of thermodynamics states that the entropy of the universe increases during all real processes, where entropy can be described as the degree of disorder. The traditional narrative is that thermodynamics was developed by the Victorians; however, I think that the ancient Greeks had a pretty good understanding of it without calling it thermodynamics.  Heraclitus (c. 535 BCE – c. 475 BCE) understood that everything is in flux and nothing is at rest so that the world is one colossal process.  This concept comes close to the modern interpretation of the second of law of thermodynamics in which the entropy in the universe is constantly increasing leading to continuous change.  Heraclitus just did not state the direction of flux.  Unfortunately, Plato (c. 429 BCE – c. 347 BCE) did not agree with Heraclitus, but thought that some divine intervention had imposed order on pre-existing chaos to create an ordered universe, which precludes a constant flux and probably set back Western thought for a couple of millennia.  However, it seems likely that in the 17th century, Newton (1643 – 1727) and Leibniz (1646 – 1716), when they independently invented calculus, had more than an inkling about everything being in flux.  In the 18th century, the pioneering geologist James Hutton (1726 – 1797), while examining the tilted layers of the cliff at Siccar Point in Berwickshire, realised that the Earth was not simply created but instead is in a state of constant flux.  His ideas were spurned at the time and he was accused of atheism.  Boltzmann also had to vigorously defend his ideas to such an extent that his mental health deteriorated and he committed suicide while on vacation with his wife and daughter.  Today, it is widely accepted that the second law of thermodynamics governs all natural and synthetic processes, and many people have heard of entropy [see ‘Entropy on the brain’ on November 29th, 2017] but far fewer understand it [see ‘Two cultures’ on March 5th, 2013].  It is perhaps still controversial to talk about the theoretical long-term consequence of the second law, which is cosmic heat death corresponding to an equilibrium state of maximum entropy and uniform temperature across the universe such that nothing happens and life cannot exist [see ‘Will it all be over soon?’ on November 2nd, 2016].  This concept caused problems to 19th century thinkers, particular James Clerk Maxwell (1831 – 1979), and even perhaps to Plato who theorised two worlds in his theory of forms, one unchanging and the other in constant change, maybe in an effort to dodge the potential implications of degeneration of the universe into chaos.

Image: decaying ruins of Fountains Abbey beside the River Skell.  Heraclitus is reported to have said ‘no man ever steps twice into the same river; for it’s not the same river and he’s not the same man’.

Consensus is just a coffee break

milk in coffee‘Consensus is just a coffee break’ to quote Caputo. He argued that if consensus was the ultimate aim then eventually we would all stop talking. The goal of conversation would be silence and as he wrote that would be a strange outcome for a species defined by its ability to speak. It is differences that drive everything: innovation, progress and the processes of life.

In thermodynamics, William Thomson (Lord Kelvin) observed that heat flows into the random motion of molecules and is never recovered, so that eventually a universe of uniform temperature will be created. When heat flows between matter at different temperatures we can extract work, for instance, using a heat engine. No work could be extracted from a universe of uniform temperature and so nothing would happen. Life would cease and there would be cosmic death [see my posts entitled ‘Will it all be over soon‘ on November 2nd, 2016 and ‘Cosmic Heat Death‘ on February 18th, 2015].

In the Hitchhiker’s Guide to the Galaxy, the crew of the Heart of Gold contemplated whether relationships between people were susceptible to the same laws that governed the relationships between atoms and molecules. The answer would appear to be affirmative in terms of dissonance being necessary for action.

So, we should celebrate and respect the differences in our communities. They are essential for a functioning, vibrant and successful society – without them life would not just consist of silent conversations but would cease completely.

Sources:

Caputo JD, Truth: Philosophy in Transit, London: Penguin 2013

Douglas Adams, The Hitchhiker’s Guide to the Galaxy, London: Picador, 2002.

More on white dwarfs and existentialism

Image by Sarah

Image by Sarah

When I was writing about cosmic heat death a couple of weeks ago [see ‘Will it all be over soon?’ posted on November 2nd, 2016], I implied that our sun would expire on a shorter timescale of about 4 to 5 billion years but without mentioning what we expect to happen.  The gravitational field associated with every piece of matter is proportional to the mass of the piece of matter and inversely proportional to distance from its centre.  The size of the sun implies it should collapse under its own gravitational forces, except that the fusion of hydrogen in its core causes an outwards heat transfer, which prevents this from happening. The sun remains a sphere of hot gases with diameter of about 864,000 miles by ‘burning’ hydrogen.  When the hydrogen runs out, the gravitational field will take over and the sun is expected to collapse to a 30,000 mile diameter ball of atoms and free electrons, or a white dwarf.

These are all spontaneous processes and so the total entropy must increase although there are some local reductions.  The heat dissipated following the fusion of two hydrogen nuclei generates more entropy in the surroundings than the local reduction caused by the fusion.  The collapse to white dwarf would appear to represent a substantial reduction of entropy of the sun because the atomic particles are crushed together. However, this is countered by the release of photons to the surroundings which ensures that the entropy of the surroundings increases sufficiently to satisfy the second law of thermodynamics.

Source:

Isaac Asimov, The roving mind: a panoramic view of fringe science, technology, and the society of the future, London: Oxford University Press, 1987.

An extract is available in John Carey (editor), The Faber Book of Science, London: Faber & Faber, 2005.