What caused the expanding universe to cool? (It may not be what you think)

Expansion leads to cooling. That’s what I was taught anyway. And so when I read that the expansion following the Big Bang caused the universe to cool, I first thought, “okay…” But then I thought some more. “Wait a minute! Expansion against what???”

The reason a system cools as it expands it that it pushes against something. For example, as a gas pushes a piston outward, the molecules recoil at a slower speed and cooling results. But there is no such piston at work in the universe. There is no boundary that the universe expands against. So why then did the universe cool?

As the universe expanded, space itself stretched and this in turn stretched the wavelengths of the photons, causing their energies to decrease and the universe to cool. The increasing wavelength of photons with increasing expansion of the universe follows from application of Einstein’s General Theory of Relativity.  But this then begs another question:  how does the resulting energy balance work?  Where does the energy lost by the photons end up going?

I had to turn to an expert on this topic for final say, namely Dr. Katherine Holcomb, who co-authored Foundations of Modern Cosmology with John Hawley and is currently a Computational Research Consultant at University of Virginia. In 2019 Katherine very generously responded to my inquiry:

Where does the energy lost by the photons go? It seems to just disappear, but that is incompatible with energy conservation. However, we do not currently understand whether the law of conservation of energy applies to the universe as a whole or what a consistent definition of the total energy of the universe might be. Perhaps further research into the nature of space and time will explain this mystery.

And there you have it!

Thank you for reading my post about this interesting challenge of the conservation of energy. I into much greater detail about energy and its conservation in Chapter 5 of my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics.

The neutron: unsung hero of the periodic table

Neutrons: The Glue That Holds the Nucleus Together

It was a race against time. The Big Bang released protons, neutrons, electrons, and photons into the newly generated and rapidly expanding universe. With a half-life of only 10 minutes, though, the free neutrons rapidly plummeted toward extinction. What saved them? The protons! As detailed by Steven Weinberg in his excellent book, “The First Three Minutes,” the protons snapped up the neutrons within 10 minutes to form deuterium particles; neutrons combined with protons in this manner don’t decay. The deuterium particles then combined with each other to create the stable helium-4 nucleus, thus laying the groundwork for the later creation of the periodic table inside the stars as recounted here.

Why were the nearly-extinct neutrons “heroes” as opposed to simply survivors? Because of this: proton-proton nuclei aren’t stable. You can’t build the periodic table on protons alone.

Two forces are at play inside the nucleus: 1) electromagnetic repulsion between the positively charge protons, and 2) strong interaction attraction between all protons and neutrons. The proton-proton nucleus has too much of (1) and not enough of (2) to remain stable. The presence of neutrons increases (2) without affecting (1). And this is why the neutrons are the glue that holds the nucleus together and why the neutrons enabled creation of the periodic table.

In general, we don’t learn about this role of the neutron in school as center stage belongs primarily to the the chemistry of the electrons and then to the number of protons, which locates each element in its proper position in the periodic table. Yes, we bring in discussion of the neutron to explain the presence of isotopes but I’m not sure we spend time explaining or otherwise celebrating its glue-like tendency.

There’s another aspect of the neutron that supports the unsung hero claim. But first a short historical background to set the context.

The Discovery of the Neutron: A Turning Point in Physics

The year 1928 welcomed the arrival of quantum mechanics, which largely focused on the behavior of electrons about the nucleus. But did you know that all of this intense mathematical and experimental work was done prior to the discovery of the neutron?

You see, at this time physicists hypothesized that the nucleus contained only protons and electrons. For example, they assumed that the helium-4 nucleus consisted of four protons and two electrons, thus matching the atomic weight of 4 (electrons have negligibly low mass relative to protons) and the net atomic charge of +2 needed to neutralize the -2 charge of the orbital electrons. Since most experiments involving the disintegration of the nucleus resulted in the emission of either alpha particles (He-4 nucleus) or beta particles (electrons), there was no reason to think that any particles other than protons and electrons comprised the atom’s center or the atom itself, for that matter. It was in response to this situation that Otto Frisch wrote, “The complacency of 1930—the widespread belief that physics was nearly complete—was shattered by the discovery of subatomic particles.” [1]

Neutrons as Atomic Projectiles: A New Branch of Physics

In 1932 at the Cavendish laboratory, James Chadwick (1891-1974) discovered subatomic particles nearly identical to the weight of the proton and deduced that they must be electrically neutral on account of their showing high penetrating power into the electrically-charged environment around the nucleus. The realization of the neutron as the final significant elementary particle of the atom, until the discovery of the quark in the 1970s, quickly solidified the terminology of atoms and helped clarify the differences between atomic number, atomic weight, and isotopes.

The neutrality of the neutron subsequently inspired Enrico Fermi (1901-1954) to propose its use as an improvement over alpha particles as atomic projectiles. The positive charge of the alpha particles repels them from the positively charged nucleus; thus, only high-energy alpha particles stand a chance of penetrating the nucleus.  The neutron, on the other hand, has no charge and can easily pass through the nucleus’ defenses without the need for high speed. 

Latching onto Fermi’s idea, the team of Otto Hahn (1879-1968) and Lise Meitner (1878-1968) opened a new branch of physics when they started firing neutrons at different elements to study the radioactive disintegration process, uranium being a favorite target. Over the course of their program, they surprisingly found that the reactions seemed more probable the slower (less energetic) the neutron projectiles were, exactly opposite what they expected.  At this time, most physicists felt that the disintegration resulting from such bombardments was caused by the physical smashing of one particle into another, much like a high speed bullet would shatter a rock.  But Hahn and Meitner’s results suggested otherwise.  It was the slow speed bullet that was the most effective. And it was the slow speed neutron that penetrated the uranium nucleus, caused it to split, and led to the discovery of fission. Another story for another time.

Thank you for reading my post about the neutron. I go into much greater detail about the atomic theory in Chapters 3 and 4 of my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics.


[1] Frisch, Otto, The Nature of Matter, 1978, p. 428.

My personal stories on those who inspired me

Several individuals inspired me in my journey to create a new thermodynamics based on the atomic theory of matter. Their collective inspiration manifests itself throughout my book, especially in Chapters 3 and 4 on the science and the history of the atom, respectively. Who were these individuals? Naturally Richard Feynman, whom I’ve quoted before (here)…

All things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied

Also, two of my MIT Chemical Engineering professors as manifested by these two events. The first was a hallway conversation I had with Professor Preetinder Virk in which I asked him why a certain physical phenomenon happened the way that it did. Professor Virk replied, to the best of my recall, “Ah, that is the ultimate goal, isn’t it? To connect the micro with the macro!” The second was in Professor Charles Cooney’s classroom. He was working through one of his assigned homework problems and said, again to the best of my recall, “The way to approach this problem is to first picture yourself as the molecule. What do you see?” The memories of both events remained deep inside my mind for many years.

On top of this was a story shared with me by the late Dr. Samuel Fleming, a very energetic and passionate fellow alumnus of MIT’s School of Chemical Engineering Practice. Sam recounted the following story to me about a lecture he attended while a student at MIT.

“T. K. Sherwood himself, no slouch when it came to mathematics and models in chemical engineering, observed at a doctoral seminar, grinning broadly, ‘Well, the trouble with these mathematical models is that if they begin to work, pretty soon you start to believe them.’ And then after the laughter died down, he turned deadly serious and asked the student presenter, ‘What are the molecules doing?’” Sam told me that he was sitting right behind TKS and never forgot the moment of the “Sherwood Axiom.”

I wrote on the science of the atom in Chapter 3 of my book. See the chapter here: Google books link, pp. 32-51. If you are seeking a very readable and personal account of both the science and the history behind the atom, I highly recommend Abraham Pais’s Inward Bound.

Impactful illustrations of scientific concepts

I took a wonderful one-day seminar by Edward Tufte a long while ago titled “Analyzing/Presenting Data/Information” and was blown away by the possibilities he opened inside my mind. I walked out of the seminar deeply inspired to create illustrations for my book beyond the standard linear timelines and black & white photos of the early scientists; I set a goal to include neither. I had rough, abstract ideas but lacked an artist to transform these ideas into illustrations. And then, through the recommendation of a friend, I discovered Carly Sanker, a wonderfully creative artist who had essentially zero background in thermodynamics. In her own words:

“When Bob first called me in March of 2018. I was living in San Francisco and for about two hours I stared out at the bay, pacing back and forth, looking out at the water, listening and talking, but mostly listening.

He explained his reasoning and the research that went into his book and he walked me through his vision for the illustrations—some of which he said had never been created. I was as excited as I was intimidated. Thermodynamics is so complex, it almost seems out of reach, I thought. Actually, he corrected me—it’s so complex that most experts with their PhDs in physics still struggle to truly understand the foundational concepts—so don’t feel bad. Now that blew my mind. Suddenly the problem seemed approachable: it wasn’t an information problem, it was a communication problem. The solution was already there, we just had to reveal it. I could handle that.

I dove in and Bob threw me a lifesaver. I was able to understand some of the simpler concepts touched on in the book from my high school physics career, but in the end I would require an on-site Professor Hanlon three-day “crash course” on thermodynamics—if you can imagine such a thing—in a shared workspace on Miami Beach of all places. It seemed like a lot to take on, because it was—but the secret to success was our focus on removing the tangential and revealing the essential. We would spend the following year creating, reviewing, simplifying and revising every illustration until for the umpteenth time we both said “ok, I think we’re actually really, finally done this time.”

I want to draw your attention to the set of my favorite illustrations of Carly’s, The Discovery Maps. I knew I wanted to created a timeline of milestone events for each of my book’s four parts: The Big Bang, The Atom, Energy, and Entropy, but again, wanted to create something new as opposed to the traditional linear approach. Carly and I worked together to create flowing, very non-linear timelines that invite the reader to discover how the history all came together for each of these parts. Carly aptly called these illustrations Discovery Maps.

You can check out the Discovery Map we created to tell the history of the Big Bang in the google books link (here, p. 2 on the left side of the open book, p. 3 on the right) and you can also check out 1) the beautiful & colorful cover Carly created, and 2) an encompassing illustrated chemistry of both the Big Bang and the subsequent nucleosynthesis of the elements in the stars (same link, p. 8). All told, 32 original Discovery Maps and illustrations populate my book. We hope you’ll enjoy them!

Thank you again, Carly!

The Big Bang, Thermodynamics, and Silos

“It is difficult to see why the book starts with a chapter on the big bang and nuclear synthesis, which were considered and understood well after thermodynamics was born. For my own taste, I would simply eliminate the big-bang chapters.” – early reviewer of my book

Oxford University Press did an absolutely wonderful job in guiding my book through the entire publishing process. This included their invitations to experts in the field of thermodynamics to assess the suitability of my book for publication. Positive feedback from these reviewers culminated in the OUP’s decision to move forward.

In this post I wanted to share with you the above comment from one of the reviewers. Why include the Big Bang in a thermodynamics book? Great question! Here was my response back to OUP.

“Regarding discussion around Part I (Big Bang) and Part II (The Atom), I have never seen the science on the origin and behaviors of atoms included in a book on thermodynamics and feel that my unique approach will lead readers to a better understanding of thermodynamics based on physical concepts.”

I expanded on this in my book itself with the following:

“Why did I include the story of the Big Bang in this book? First, because it explains the origins and populations of the elements in the periodic table. Second, because the world of astronomy rarely overlaps with the world of physics, chemistry and engineering, and perhaps something, some opportunity to gain insight, is lost because of this. Our division of science and engineering into different camps serves a purpose—we can’t study everything—but perhaps this does us an injustice as it narrows our view and hence our understanding and hence our ability to explore and create.”

The silo walls between the fields of science and engineering can be very thick. I believe that breaking these walls down and merging the content into one seamless integrated whole would make for a wonderful and more effective educational experience.

What do you think?

Full access to Block by Block’s Chapter 1: The Big Bang/Science is available on google books here (pp. 5-11).

Why the Mark Helprin quote in my Introduction?

Full access to Block by Block’s Introduction—and then some! they certainly share a lot!—is available on google books here (pp. xiii-xx). The Introduction shares the motivations that drove me along with the structure I created to guide me. In keeping with the intent of the series of posts I plan on publishing for the foreseeable future, which is to highlight a single idea from each chapter from my book, I want to draw your attention to the following quote that I used in the Introduction:

People say, Think if we hadn’t discovered Emily Dickinson. I say, Think of all the Emily Dickinsons we’ve never discovered” – Catherine Thomas Hale character in Mark Helprin’s In Sunlight and in Shadow

I chose this quote for two reasons, the first being that Mark Helprin is one of my favorite authors. A Soldier of the Great War, Winter’s Tale, Refiner’s Fire. Beautiful, magical writing. Of the many, many quotes I could have used, I chose the above because of my second reason: it captured the historical reality of thermodynamics.

I feel for those who toiled away at the experimentalist’s lab bench or the theoretician’s desk and generated results that were ignored by history. So many individuals were involved in creating the new field of thermodynamics, but we only see the few. This post is a simple but deeply felt acknowledgment to all of those “Emily Dickinsons” we never discovered.

Don’t let your friends off the hook. Challenge them to take action on their dreams.


Me: I think I want to write a book.
Friend: Does that mean you’re going to write it?
Me: (to myself) oh no
Me: (with sweating palms) Yes

I shared a someday-maybe dream with a friend and she challenged me. “Are you going to do it or not?” When I said, with some fear of the task in front me, “yes!”, she pulled out a scrap piece of paper and wrote, “Write that book!” I’ve kept it in my wallet ever since (see above foto). An ongoing inspiration to his day.

Consider being a listener for your friends’ dreams. Be ready to challenge them to commit. If they’re thinking about doing something that they’re passionate about, do what you can to have them transform the thought into action. They’ll appreciate it.

To my friend from a long time ago: Thank you!

P.S. Some would argue that the work isn’t done until you follow through and help your friends to achieve their dreams, whatever that might look like for you.

Gibbs free energy: G or ∆G?

One of my objectives in creating a more effective approach to teaching thermodynamics is to bring clarity to some of the confusing terms and concepts embedded in this field. Initially I focused on the concept of heat by pointing out that there is no such thing. I now turn toward free energy.

As a very (very) brief historical summary, Rudolf Clausius created what became known as the 1st Law of Thermodynamics, which I wrote about here, based on energy and its conservation when he wrote the equation: dU = TdS – PdV [1]. J. Willard Gibbs then built upon this by creating a new property of matter, later to be given the symbol G after Gibbs, for which G = H – TS [2]. This energy term became very useful in thermodynamic analyses of physical phenomena and industrial processes that occur at constant temperature and pressure. Of relevance to this post, Gibbs showed that the change in G at constant T,P quantifies the maximum amount of work that can be generated by a given process such as a chemical reaction.

Prominent thermodynamics textbooks, such as Lewis and Randall [3, p. 158] and Smith and van Ness [4, p. 170], named G free energy. Today we often refer to G as Gibbs free energy and associate it with the amount of energy that is free to do useful work.


Naming G free energy always confused me. While certain thermodynamic properties such as temperature, pressure, and mass are absolute, meaning that they can be referenced to zero, the property internal energy (U) is not. There is no zero for internal energy, which is why the primary focus in thermodynamics is based on changes and not absolutes. We’re largely concerned with changes in energy; absolute energy doesn’t exist. Thus, Gibbs’s G property, which is based on energy since it includes internal energy U, i.e., G = H – TS = U + PV – TS, is meaningless on its own. This is the reason for my confusion with naming G free energy. Free energy has meaning, while G itself does not.

Consider the intent of the two founders of “free energy” – Gibbs & Helmholtz [5]

To Gibbs, it’s the change in G that’s meaningful, not G itself. It is the distance between a given body’s non-equilibrated energy—non-equilibrated in the sense that the body is either not internally equilibrated or not equilibrated with the environment or both—and its equilibrium state energy that was important to Gibbs. He called this distance, which quantified change, “available energy” [6, pp. 49-54]. Today we view available energy and free energy as synonyms.

Hermann von Helmholtz created his own energy term A = U – TS, which served a similar purpose as Gibb’s G, but for constant temperature processes as opposed to constant temperature and pressure for Gibbs. It was Helmholtz who coined the term “free energy” as shown here from his publication on the matter [7]:

It has long been known that there are chemical processes which occur spontaneously and proceed without external force, and in which cold is produced. Of these processes the customary theoretical treatment, which deals only with the heat developed as the measure of the work-value of the chemical forces of affinity, can give no satisfactory account.

Here Helmholtz is referring to the Thomsen-Berthelot theory of thermal affinity, for which the “heat developed” is quantified by ∆H, the enthalpy change of reaction. This theory suggested that cold-producing endothermic reactions (∆H > 0) should not happen; and yet they did. Continuing…

If we now take into consideration that chemical forces can produce not merely heat but also other forms of energy… then it appears to me unquestionable that… a distinction must be made between the parts of their forces of affinity capable of free transformation into other forms of work, and the parts producible only as heat. In what follows I shall, for the sake of brevity, distinguish these two parts of the energy as the “free” and and as the “bound” energy.

It is clear to me that Helmholtz sought to replace ∆H with a term that quantified his concept of “free” energy. This term had to be similar to ∆H in that it had to quantify change as opposed to absolute. This is how he arrived at ∆A.

In Sum: Free energy was founded on change

That both Gibbs and Helmholtz based their respective concepts of free energy on change as opposed to absolute supports my contention is that G should be known as Gibbs energy and ∆G should be known as Gibbs free energy. In other words: Gibbs free energy (∆G) is the change in Gibbs energy (G).

I propose that textbooks make clear these definitions, especially since some confusingly refer to G as both Gibbs energy and Gibbs free energy. Is the above argument strong enough to justify this? What do you think?

Thank you for reading my post. I go into much greater detail about these concepts in my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics.


[1] dU = Q – W = TdS – PdV. Q = thermal energy added to system = TdS, W = work done by system = PdV, U = internal energy, T = temperature, S = entropy, P = pressure, V = volume. If no thermal energy (i.e., heat) is added to the system and if no work is done by the system, then the internal energy of the system does not change, i.e., dU = 0.

[2] G = H – TS. H = enthalpy = U + PV. The change in G is thus: dG = dH – d(TS) = dU + PdV + VdP – TdS – SdT. For a constant temperature and pressure process, dT = dP = 0. If the system of interest is equilibrated then dU + PdV – TdS = 0, and thus dG = 0. The property G is particularly useful when considering phase equilibrium. Consider two phases, A and B, in equilibrium with each other. The values of G for the two phases are equal. If you change temperature and pressure together so as to maintain a two phase system, again dU + PdV – TdS = 0 as it’s an equilibrated system, and so dG = VdP – SdT. One can show that dG for A must equal dG for the B. With some re-arrangement, dP/dT = (SB – SA)/(VB-VA), which is a version of the famed Clapeyron and Clausius-Clapeyron equations.

[3] Lewis, Gilbert Newton, and Merle Randall. 1923. Thermodynamics and the Free Energy of Chemical Species. New York: McGraw-Hill Book Company, Inc.

[4] Smith, J. M., and H. C. Van Ness. 1975. Introduction to Chemical Engineering Thermodynamics. 3d ed. McGraw-Hill Chemical Engineering Series. New York: McGraw-Hill.

[5] Gibbs cited the influence of François Massieu on his work that included the creation of G = H – TS.

[6] Gibbs, J. Willard. 1993. The Scientific Papers of J. Willard Gibbs. Volume One Thermodynamics, Woodbridge, Conn: Ox Bow Press. p. 51.

[7] Helmholtz, H. von, On the thermodynamics of chemical processes, Physical memoirs selected and translated from foreign sources 1 (1882): 43-97.


Pauli exclusion is not a repulsive force, and yet…

It’s not a force.” – Professor Steven Weinberg

I made a mistake.

In my book, Block by Block, I wrote about the attraction and repulsion forces between atoms. For the former, I stated that attraction results from the fact that atoms act like spinning magnets; they contain a positive charge (proton) that is separated from an orbiting negative charge (electron). The quickly varying dipole of one atom acts upon the same of another atom, thereby inducing dipoles that are in-phase with each other. The electrons of atoms attract the protons of other atoms, resulting in an attractive force between all atoms. This phenomenon is all very nicely laid out in a paper by F. W. London [1], who coined the term “dispersion effect.” But this wasn’t where I made a mistake.

The mistake was with my supposed understanding of the repulsion forces. On page 46 of my book I wrote that repulsion is caused by “the electromagnetic repulsion forces between electrons and between protons.” This might not look like a mistake to you, but it does to me, or at a minimum, as an incomplete answer, because I now know something I didn’t fully understand then. You see, I understood that Pauli exclusion was somehow involved in the repulsion effect but didn’t know why. I originally wondered whether or not it was a repulsive force itself. When I couldn’t find the answer I was seeking in the literature, I decided to go straight to the top for help. Professor Steven Weinberg at University of Texas at Austin. I was pleasantly shocked when he very kindly replied! In response to my question regarding whether or not Pauli exclusion is a force, Professor Weinberg replied, “It’s not a force.” To this day I remember that one line from his reply. He continued:

There is no particle transmitted between the electrons in an atom other than the photons, which mediate the electromagnetic force. But the Pauli principle requires that the wave function of the atom be antisymmetric in the electron coordinates, and this has effects like a force – – – in particular, it prevents two electrons from occupying the same state.” [2]

As I recently began work on book #2, seeking to connect the micro-world of atoms to the macro-world of classical thermodynamics, I knew I had to resolve this issue as I consider it a very fundamental building block for the larger structure I want to create. Over the past two weeks I have done a deep dive into the literature, and here’s what I have found.

First things first. The Pauli exclusion principle states that no two particles can have the same four quantum numbers, which for orbital electrons translates into fact that no more than two electrons are permitted in any given orbit, and the two must have opposite spins.

Next. Electrostatic interactions, e.g., attraction and repulsion, are determined by the electron distribution. Again, the attraction force is caused by London dispersion, which is the induced shift in electron distributions that occurs when two atoms come near each other.

Regarding repulsion

Regarding repulsion. Let’s start with two simple hydrogen atoms approaching each other. Each atom consists of one proton and one electron. As they approach, their respective electron clouds overlap and the individual atomic orbitals of each merge into a bonding orbital. Both electrons populate this single orbital and then spend most of their time between the two nuclei, attracting both nuclei toward them and toward each other. A covalent bond results. No bond is stronger as emphasized by Richard Feynman: ‘‘It now becomes clear why the strongest and most important attractive forces arise when there is a concentration of charge between two nuclei. The nuclei on each side of the concentrated charge are each strongly attracted to it.’’ [3]

Now consider two helium atoms approaching each other. Each atom consists of two protons, two neutrons, and two electrons. As they approach, their respective electron clouds overlap, and their individual orbitals merge into a bonding orbital, which is then populated by two of the electrons, one from each atom.

Now comes the critical part of this post. What happens to the next two electrons? They can’t enter into this same bonding orbital with the others because of the Pauli exclusion principle. So they must enter into the next orbital available up on the energy ladder, which is an anti-bonding orbital. This orbital forms at the same time as the bonding orbital. The anti-bonding orbital is so named because the electrons in this orbital accumulate outside the region between the nuclei and so can’t contribute to bonding. Instead they contribute to anti-bonding since their location effectively decreases the pull of the two positively-charge nuclei toward the negative electrons between them, leaving the proton-proton repulsion force to dominate the situation.

The anti-bond negates the covalent-bond, leaving a very weak net bond. This is what happens when atoms “collide.” The bond between them is weak and they repel each other. Electron-electron interactions contribute to the net repulsion, but it’s the proton-proton interactions that dominates. Two helium atoms collide (and don’t react) because there is room in the bonding orbital for only one pair of electrons; the other pair must occupy the anti-bonding orbital.

The same general principles apply to all closed-shell molecules. Individual electron orbitals combine to form two orbitals, one bonding and one anti-bonding. Being closed-shell, two electrons are offered up by each atom. Two enter the bonding orbital, the other two the anti-bonding orbital, leaving a weak net bond that is easily broken by the strong proton-proton repulsion.

In the end, while Pauli exclusion doesn’t directly cause repulsion, and is not a repulsive force, it is because of Pauli exclusion that repulsion occurs.

I list three excellent references below that go into much greater detail on this matter: Henry Margenau [4], H.C. Longuet-Higgins [5], and Richard Bader [6]. I saw that Professor Bader’s 2007 paper was relatively recent and sought to contact him. I learned that he had passed in 2012 but noted that one of his students co-authored a relevant paper of his. It was through this path that I met this student, Chérif F. Matta. Chérif is Professor and Chair/Head of the Department of Chemistry and Physics at Mount Saint Vincent University in Halifax. He enthusiastically responded to my email inquiry and helped me with my understanding of the above topic; any mistakes above are all mine! I publicly thank him here for his contribution and look forward to further discussions with him.

(1) London, F. W., The General Theory of Molecular Forces, Trans. Faraday Soc., 1937,33, 8b-26. This paper, by the way, shows the origin of the r^6 attraction term in the Lennard-Jones potential equation.

(2) Weinberg, Steve, personal communication, 01 July 2009.

(3) Feynman, R. P., Forces in Molecules, Physical Review, 56, 15 August 1939, pp. 340-343.

(4) Margenau, Henry, The Nature of Physical Reality, McGraw Hill, 1950. Chapter 20, The Exclusion Principle, pp. 427-447.

(5) Longuet-Higgins, H. C., Intermolecular Forces, Spiers Memorial Lecture, The University, Cambridge, Received 23rd September, 1965, published in Discuss. Faraday Soc., 1965,40, 7-18

(6) Bader, R. F. W., J. Hernández-Trujillo, and F. Cortés-GuzmánBader, Chemical Bonding: From Lewis to Atoms in Molecules, J. Comput. Chem.. 2007 Jan 15;28(1):4-14

Thank you for reading my post. I go into much greater detail about the science and history of the atomic theory in Chapters 3 and 4, respectively, of my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics.

Career decision making – trust your gut

When I give thermodynamics presentations to high school and college students, I begin with a 10-minute discussion about career decision-making based on my own experiences. I now share this discussion with you, both to provide you with helpful and hopefully inspiring ideas and to also seek your feedback. Do your thoughts align with mine? Let me know! [Note: the examples I use are from my academic years to align with the students, but the process I lay out applies to my entire career.]


Are you trying to decide what to do for your summer internship, your first job, the opportunity to switch jobs, to retire, or to accept an overseas assignment? If you are, I’m guessing you’re experiencing some degree of overwhelm. Here’s why.


“…one of the most difficult types of emotional labor is staring into the abyss of choice and picking a path.” – Seth Godin, Linchpin, p. 57.

Fear of living without a map is the main reason people are so insistent that we tell them what to do. – Seth Godin, Linchpin, p. 125

Because you have options, you have choice, and that can be a source of overwhelm. Choice is both a blessing and a curse. Wouldn’t life would be so much simpler if someone told you what to do, what decisions to make? Yes. But wouldn’t that be rather boring? And who exactly would tell you what to do? Who knows you better than you? Sure, your parents might weigh in early in life, but at some point, it’s your choice, and that choice can be overwhelming, as well manifested by this scene with Robin Williams from Moscow on the Hudson. The goal then is to develop an approach to reduce the overwhelm by transforming the decision-making process from scary to exciting. Here’s how I did this. Maybe it will work for you.

Maslow’s Pyramid

In 1943 American psychologist Abraham Maslow proposed a priority sequence for human motivation. As later illustrated by others (to the right), humans are only motivated at each stage in sequence up the pyramid once they feel satisfied with the stage they’re in. It’s very hard to worry about feelings of accomplishment when you’re worried about where your next meal is coming from.

Survive then Thrive

For my career decision-making, I took Maslow’s pyramid and simplified it. I wasn’t aware that this is what I was doing in my early years. I’m only recognizing it now. When I had to make a decision, my first priority was survival. Once I felt comfortable with that, and narrowed down the field of options, I then made my final decision based on my desire to thrive. Let me explain this process in more detail.


For each individual career decision, I had a range of options to choose from. At times, yes, it was overwhelming. But in the end I was able to narrow down the number of options by first passing them through my “survive” filter. To me, survival meant financial independence. Each career decision took me toward financial independence, the point at which I no longer had to work for somebody else. Some of these decision didn’t earn me more money but instead earned me experiences that I knew would lead to higher-earning opportunities later on. Note the additional criteria I added to my “survive” filter: whatever it was I chose had to be something I was good at and enjoyed doing.


There is no intellectualizing what resonates with you… When it reveals itself, you feel it. – Ryder Carroll, The Bullet Journal Method, p. 146.

The now-smaller list of options met up with my second “thrive” filter. This filter was governed by what I was passionate about, and the part of my body that best understood this was my gut. When a select group of “survive” choices came in front of me, I invariably knew, without necessarily knowing why, the one I wanted…as well as the one(s) I didn’t want. The one I wanted resonated with me, especially if it offered me the opportunity to journey on the road less traveled.

At some point, you have to make the decision

The important point I emphasize in the above illustration is the final red dot. At some point in the process I realized I had to make a decision, both to move forward and to gain experience. Sometimes the decision may have been to stay put, as this is always an option. But even with this seemingly non-decision decision, my choice to stay put was often accompanied by a decision to make a stronger commitment to what I was then doing.

Failure is guaranteed if you never begin – Ryder Carroll, The Bullet Journal Method, p. 125.

There is no “right” decision

The “thrive” decision was admittedly hard at times. Why? Because I often felt that a “right” decision existed and that my life would be forever damaged if I didn’t choose it. I now realize, in hindsight, that this is false. There is no “right” decision in my “thrive” filter. Once I realized this, it helped keep “analysis paralysis” at bay. Each decision leads down a different path, and for the most part, each path will work out just fine. They’ll just be different, that’s all.

Why I chose Bucknell University

For example, I considered a range of undergraduate universities: Bucknell, Lehigh, Clarkson, RPI. They were all good. I would have enjoyed any of them, each in a different way. Why did I choose Bucknell? Well, because when I visited the campus during high school spring break with my parents, Bucknell’s cherry blossoms were in full bloom–in hindsight, I think the grounds keepers somehow ensured this as it was spring break visit week!–and this sold me. Something in me clicked. My gut told me that Bucknell would work for me. I couldn’t list the reasons. The beauty of those trees played a role, perhaps. But I think there was much more to it than that. Sometimes decisions from the gut bypass the brain. All the experiences that I had in my life up until then, including the conversations with others and especially my parents, led me to that decision.

More experiences = better gut feel

This brings me to the curved arrow going from decision to experience. To me, the more decisions one makes, the more experiences one gains, and the better the gut feel develops. Gut feel doesn’t develop in a vacuum.

When you come to a fork in the road, take it – wisdom shared by a friend

Listening to your gut feel is so important when making career decisions. When considering the final decision from a range of options, you often just simply know deep down which decision you want. You feel it in your body. Trust this feeling. Use it to guide whether to do something… or not.

Consider the following, as described by Russ Roberts in his engaging book Wild Problems (p. 44). If you have to decide between two options, flip a coin, and while the coin is still spinning in the air, note which side you are hoping will come up. In that moment, you’ll realize that you don’t even need to see the outcome, because your decision will have already become clear to you. Trust your emotions. You don’t need to explain them to yourself or to others.

Why I went to Karlsruhe

As a final example of how this process worked for me, consider my decision to do a post-doctorate research project in Karlsruhe, Germany.

Remember those various display cases lining university hallways? They contain all sorts of interesting information. It was a rare occasion when I would stop and read, but all it took was once. I was walking down the MIT hallway, thinking about what company I was interested in joining upon graduation, when, for some unknown reason, I stopped at a case similar to the one on the right and actually read what was in it. A flyer spoke of scholarships offered by the German government to do post-graduate work at one of their universities. Bam! It hit me. I had never considered this before then. And all of a sudden it went to the top of my list.

Where did this decision come from? It came from everything, all of my experiences. My conversations with foreign students at MIT, the movies I watched, the stories from my dad about his international travel for Bristol-Myers, my interest in taking the fork, the road less traveled, the once-in-a-lifetime opportunity to live in a foreign country, not with a group, but on my own, knowing it would force me to learn the language. So many different experiences primed my gut to tell me, “Apply”. And I did. And I went. And I never looked back. This decision provided me with another experience, a big experience, that further developed my gut feel for the decisions I would be making later on in my life.

Final thoughts

The survive-then-thrive approach indeed helped me to manage the overwhelm during my career decision-making process. Along the way I learned to trust my gut more and more. How did you approach your own decision making process? The same? Different? If you do try out any of these ideas, please let me know. In the meantime, thank you for reading my post. While I don’t specifically discuss the above concepts in my recently published book Block by Block – The Historical and Theoretical Foundations of Thermodynamics, they do make for a stimulating starting point for an engaging conversation around what motivated the early thermodynamics scientists in the directions they took in their own lives?