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.
“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.