I mentioned a couple of weeks ago that I am teaching thermodynamics at the moment [see ‘Conversations about engineering over dinner and a haircut‘ on February 16th, 2022]. I am using a blended approach [see ‘ Blended learning environments‘ on November 14th, 2018] to deliver the module to more than 300 first year undergraduate students with one hour in the lecture theatre each week while the students follow the components of the MOOC I developed some years ago [see ‘Free: Energy! Thermodynamics in Everyday Life‘ on November 11th, 2015, and ‘Engaging learners online‘ on May 25th, 2016]. I have found that first year undergraduates are reluctant to participate in the online discussions that are part of the MOOC and so last year I asked them to discuss each topic in small groups with their academic tutor. I got some very positive feedback from tutors who had interesting and stimulating discussions with their students. We are repeating the process again this year. The first discussion is about energy transformations: noting that energy is always conserved but constantly transformed into different forms, each student is asked to start from an energy state of their choice and to trace the transformations backwards until they can go no further. In the lecture preceding the discussion with their tutor I provide some examples for starting states, including breakfast cereal, a pole vaulter in mid-jump and a bullet train. I also describe the series of transformations from the Big Bang to tectonic plate movement: after the initial expansion caused by the Big Bang, the universe cooled sufficiently to allow the formation of sub-atomic particles followed by atoms of hydrogen and some helium and lithium that gravity caused to coalesce into clouds which became the early stars, or solar nebula. A crust formed on the solar nebula which broke away to form planets. Our planet has a molten core with temperatures varying from 4,400 to 6000 degrees Celsius, compared to around 5,500 degrees on the surface of the sun. The temperature variation in the Earth’s core cause thermal currents which drive the movement of tectonic plates and so on [see ‘The hills are shadows, and they flow from form to form, and nothing stands‘, on February 9th, 2022]. Most chains of energy transformation lead backwards to the sun and forwards to dissipation of energy into some unusable form which we might call ‘entropy’ [see ‘Life-time battle‘ on January 30th, 2013].
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.
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.
“In the quantum theory of gravity, time becomes the fourth dimension to add to the three dimensions of space (x, y, z or length, width and height), and Stephen Hawking has suggested that we consider it analogous to a sphere. Developing this analogy, we imagine time to be like a flea running around on the surface of a ping-pong ball. A continuous journey, without a beginning or an end. The ‘big bang’, frequently discussed as the beginning of everything, and the ‘big crunch’, proposed by physicists as how things will end, would be the north and south poles of the sphere. The Universe would simply exist. The radius of circles of constant distance from the poles (what we might call lines of latitude) would represent the size of the Universe. Quantum theory also requires the existence of many possible time histories of which we inhabit one. Different lines of longitude can represent these histories.
If you are not already lost (the analogy does not include a useful compass) then physicists would give you a final spin by dropping in the concept of imaginary time! Maybe it is time for the flea to jump off the ping-pong ball, but before it does, we can appreciate that it might move in one direction and then retrace its steps (or its hops if you wish to be pedantic). The flea can travel backwards because in this concept of the Universe, time has the same properties as the other dimensions of length, height and width and so it has backwards as well as forwards directions.”
This is an extract from a book called ‘The Entropy Vector: Connecting Science and Business‘ that I wrote sometime ago with Bob Handscombe. I have reproduced it here in response to questions from a number of learners in my current MOOC. The questions were initially about whether the first law of thermodynamics has implications for the universe as a closed system (i.e. one that can exchange energy but not matter with its surroundings) or as an isolated system (i.e. one that can exchange neither energy not matter with its surroundings). These questions revolve around our understanding of the universe, which I have taken to be everything in the time and space domain, and the first law implies that the energy content of the universe is constant. The expansion of the universe implies that the average energy density of the universe is getting lower, though it is not uniformly otherwise we would have reached the ‘cosmic heat death’ that I have discussed before. However, this discussion in the MOOC led to questions about what happened to the first law of thermodynamics prior to the Big Bang, which I deflected as being beyond the scope of a MOOC on Energy! Thermodynamics in Everyday Life. However, I think it deserves an answer, which is why reproduced the extract above.