Many great minds throughout history have dedicated their lives to the study of physics and progression of science and knowledge. Physicists such as Newton, Maxwell, Einstein, Planck, and Schrödinger have provided greater understanding of our universe than we could have ever believed previously. There is no doubt that their profound contributions have significantly shaped the study of physics. However, today I would like to bring light to the underrated, yet also brilliant, physicists whose contributions should receive appreciation for their significant advancements in science as well. You may have heard the saying, “Time’s arrow marches forward”, and if you have, it is thanks to physicist Ludwig Boltzmann.
Let us start by taking a look at Boltzmann’s early life and background. He was born in the middle class on February 20, 1844, in Vienna, Austria. He grew up studying mathematics and science but was truly passionate about playing piano and was taught by famous composer Anton Burckner, the Leonardo DiCaprio of the 19th century (“Sex, Death, and Dissonance”). A noteworthy event in his life is when his father died when Boltzmann was just 15. At age 19, he enrolled at the University of Vienna as a physics and math student. Only three years later, he received his PhD and started teaching at Graz. He earned a full teaching position as a professor there at just age 25 for the subject “Mathematical Physics”. For the rest of his life, he bounced around from different universities while completing research. (“The genius of disorder”)
“Boltzmann focused his research and theories on understanding the nature of heat and energy.”(“The genius of disorder”) What is interesting is that the steam engine had already been patented by James Watt, yet was still not fully understood by scientists. The origins of heat energy and its transformation processes were still unknown. Considering the impact and potential of Watt’s steam engine, heat was what you could call a “hot topic” in the scientific community.
Important questions such as, “Why do natural processes move in one direction, forward?” and “What determines the arrow of time and the expansion of the universe?” were answered by Boltzmann’s research. (“The genius of disorder”) His main interest was understanding the second law of thermodynamics. The second law states that heat flows spontaneously from hot to cold bodies based on the natural dispersion of energy. “An essential concept for Boltzmann’s work established by Benjamin Thompson [also known as the Count of Rumford] is that heat is the result of motion among the fundamental constituents of matter.” (“The genius of disorder”) Why is this an important distinction? Boltzmann’s radical vision of the world relied on the theory that the universe is made up of atoms. He also embraced the kinetic theory, that atoms are always in motion. At the time, scientists were divided about the existence of the atom. The fact that Boltzmann depended on the atomistic hypothesis being true, made his work controversial, often criticized, and challenged. “The particular complexity of Boltzmann’s studies was he had to understand macroscopic systems made up of billions and billions of particles.” (“The genius of disorder”) He believed that it was impossible to know the properties of every single particle, and therefore had to focus on understanding their macroscopic effects. To do this, he turned to probabilities. He figured that he could explain the behavior and nature of lots of little particles based on their chances of exhibiting certain properties. Now how does this concept of statistical mechanics also relate to other concepts that are explained by the second law of thermodynamics such as entropy and the direction of time? I think that the best way to explain this would be to look at some examples.
A classic example that is often used to explain the direction of time and entropy is the shattering of a coffee cup. Imagine a person holding a coffee cup a couple feet away from the ground. Now imagine dropping the coffee cup and it falling to the ground. What will happen to the delicate cup? From your experience, you can probably guess that it will break and shatter. The difference between the initial state of the cup – put together – and the final state of the cup – shattered in pieces – is the object’s entropy. Entropy in very simple terms, is the statistical probabilities of the different states of a system. (“Entropy Definition”). Systems that have higher entropy, statistically, have more ways of arranging itself. The initial state of the coffee cup has lower entropy, because those atoms that make up the cup have to be in certain order to make up the crystalline structure of the solid material in that shape; there are many less ways for the atoms to be arranged and still have that same initial state and conditions. The shattered coffee cup is considered to have higher entropy because it is the more disordered system. Now what else is important about the case of dropping a coffee cup? Another thing that you might have noticed is that you have never seen the reverse order of events. You have never seen the shattered coffee cup on the ground, reconstruct itself and leap back up into the person’s hand as if it never broke in the first place. It would be going back in time. Why is it that you have never seen this happen? Boltzmann concluded that the reason you have never seen objects go from disordered states to ordered states is because it is statistically very improbable. He came up with an equation, now known as Boltzmann’s Equation, that describes probability distribution. This is why he is known as the father of statistical mechanics. This equation is what established the development of statistical mechanics. Statistical mechanics is specifically defined as, “A branch of mechanics dealing with the application of the principles of statistics to the mechanics of a system consisting of a large number of parts having motions that differ by small steps over a large range” (“Statistical Mechanics Definition”) The equation explains how probability changes with time, which is a concept that wasn’t fully grasped until then. Theoretically, it is possible for the coffee cup’s atoms to rearrange themselves exactly back into their initial state and rebuild the coffee cup, however, the chance of this happening is so incredibly small that by the time it will have happened, the universe will no longer exist. It is exciting to know that the chances are non-zero and that theoretically it is possible. Though, this basically impossible chance of systems going from disordered to ordered states is why Boltzmann concluded that time has one direction due to the tendency of objects increasing in entropy. While energy in the universe is conserved, entropy tends to increase, which is a fundamental idea that the second law of thermodynamics is based on. This is also why “the arrow of time” only moves forward and is closely associated with the second law, because for it to move backward would mean for a system to go against the natural laws of entropy. Why did Boltzmann receive criticism for his conclusions on the second law of thermodynamics? It contradicted Newton’s fundamental laws of physics which did not define directions of time. The irreversibility of the second law and the reversibility of classical mechanics phenomena was a great contradiction and a problem for scientists. There is a paradox from the reversibility of microscopic phenomena and irreversibility of macroscopic phenomena. However, the kinetic theory of gases explains this contradiction. Each individual particle moves between its initial and final states, but the probability of every particle from the system moving back into their initial states all at the same time is highly unlikely.
What did this mean for the future of science? Since then, Boltzmann’s formula has greatly contributed to the study of black holes. (“The genius of disorder”) Max Planck was inspired by his ideas of quantization of energy to explain black body radiation. Planck stated, “I was greatly impressed by Ludwig Boltzmann’s ideas, by which I was guided when formulating the laws I discovered during my experiments.” (“The genius of disorder”) Without Boltzmann, Planck might not have been able to make the connection that energy can only be emitted in discrete quantities.
It is clear that Ludwig Boltzmann was an influential figure in the scientific community. His contributions to physics and understanding of the universe were not fully understood during his time. It is amazing what he accomplished, especially when, unfortunately, having to cope with mental illness and difficult times throughout his life. He was known to experience extreme mood swings and depression. He lost his father at a young age, had to live through the death of his first son, which caused him a severe mental breakdown, and faced criticism of his ideas and theories by other scientists. Despite all of this, he was known to be very kind, pleasant, and gentle. He was an enthusiastic and inspiring teacher at the University of Graz and tried his best not to fail any of his students, especially those with financial struggles.(“The genius of disorder”) Later in his life, his eyesight deteriorated to the point where he could no longer read, and he experienced painful migraines and respiratory problems which forced him to give up working on research.(“The genius of disorder”) In 1906 while on holiday in Italy, his daughter, Elsa, found his dead body at their hotel. On September 5, 1906, Ludwig Boltzmann’s suicide was a tragic end to his life. (“The genius of disorder”) About a year before his death, Einstein was studying Brownian Motion and found evidence supporting the atomistic hypothesis which Boltzmann advocated for throughout his entire life. Clearly, he was far ahead of his time. In his own words, “Bring forward what is true, write it so that it is clear, defend it to your last breath!” Despite the opposition he faced, that is exactly what he did. As a pioneer of atomism, his explanation for the second law of thermodynamics, use of probabilities to explain the natural phenomena of energy, and development of statistical mechanics, Ludwig Boltzmann well-earned his title as “Father of Statistical Mechanics”.
Work Cited
“Sex, Death and Dissonance: The Strange, Obsessive World of Anton Bruckner.” The Guardian, Guardian News and Media, 1 Apr. 2014, www.theguardian.com/music/2014/apr/01/sex-death-dissonance-anton-bruckner-concertgebouw-orchestra.
“Entropy Definition & Meaning.” Merriam-Webster, Merriam-Webster, www.merriam-webster.com/dictionary/entropy#:~:text=broadly%20%3A%20the%20degree%20of%20disorder,universe%20toward%20death%20and%20disorder. Accessed 2 Feb. 2024.
“Statistical Mechanics Definition & Meaning.” Merriam-Webster, Merriam-Webster, www.merriam-webster.com/dictionary/statistical%20mechanics. Accessed 2 Feb. 2024.
“Ludwig Boltzmann – The Genius of Disorder [2007].” YouTube, 2007, https://www.youtube.com/watch?v=hENRIAx-6D4. Accessed 2024.
