Bailyn's Fables: Chandrasekhar's Limit

First, we need to know a little something about white dwarfs and electron degeneracy pressure. You see, the normal way stars manage to not collapse into their incomprehensibly massive selves is thermal pressure. Basically, while gravity is pulling everything in, pressure is pushing everything back out, and so the two balance, at least, for a while. Eventually the star runs out of hydrogen in the core, which contracts, raising temperature of a shell of hydrogen outside the core, causing it to start fusing. This expands the star into a red giant, until all remaining hydrogen has been fused, making the star contract again.

What it doesn't do is collapse into a black hole. It seems that for high density objects other kinds of pressure arise. In this case it is electron-degeneracy pressure. Very, VERY basically, this is a result of no two particles being able to occupy the same space, and the pressure that results as the volume these particles are occupying decreases. Long story short is that this pressure fights against the gravity of the collapsing star, balancing at roughly the radius of the earth. This is called a white dwarf, and this is where we pick up the main subject of this post.

In the 1930s an Indian-American called Subrahmanyan Chandrasekhar discovered that electron-degeneracy pressure isn't always enough. If the mass of the star is more than 1.44 solar masses gravity overcomes the pressure and the star continues to collapse. He presented his findings to the Royal Astronomical Society. Upon finishing however Sir Arthur Eddington stood up and opposed Chadrasekhar's findings, stating:

 I think there should be a law of Nature to prevent a star from behaving in this absurd way!

A full account can be found in , pages 37-39. It is apparent that while he could understand the theoretical idea of a black hole, Eddington simply could not conceive of Chadrasekhar's findings, that beyond a certain mass a star could essentially collapse into nothing.The result of this was that a number of physicists who would otherwise have publicly agreed with Chadrasekhar did not, due to Eddington's status. Chandrasekhar spent the rest of his life holding to his beliefs, even until 50 years later when he finally got the Nobel Prize for his work.

The moral of this tale is that maybe one should believe their student, rather than their own intuition. Had Eddington allowed for Chandrasekhar's work to be possible, we might not have lost a good 40 odd years of research into black holes. It also demonstrates the dangers of being too convinced of one's own intellect. As Eddington got older he became more and more convinced that he could just guess the answer to questions using gut instinct, a method I imagine most of us would agree to be utterly useless scientifically.

Further reading

A review of the meeting in which Chandra presents his findings and Eddington tears them down. Relevent pages are 37-39
The highlights of Chandra's life
A brief biography, and image source for this post

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Bailyn's Fables

A fable, for those who for some reason never were children, is a short story, generally full of cute anthropomorphic woodland animals who have misadventures and finish the story either dead or having learned a lesson or moral.  It turns out that science is full of these stories, admittedly minus Benjamin the Bunny or whoever. These are stories that, generally speaking, describe the process of some discovery or event, but upon closer scrutiny, turn out to have an element of artistic license, as it were. While this might piss the scientific historians off somewhat, they still serve a purpose. The point is not that the story is an accurate depiction of events so much as it is a lesson, a vivid illustration of how to behave.

It is in these posts therefore that I will discuss some of these scientific fables, and while noting the morals, will perhaps delve somewhat into the truth of things.

I should explain that the name I have chosen for this series is from the Professor of Physics and Astronomy at Yale University, Charles Bailyn, from whom I will have stolen a great number of these fables. He was first brought to my attention mid 2011 when I was pointed in the direction of a number of free online lectures. Never one to pass up either free things or learning, I downloaded a number of these, one series of which was fronted by this Bailyn fellow. I quickly was impressed by his teaching style. So many lecturers I have found to be stiff and awkward in front of a large group of people, but he managed to sound enthusiastic, interested, and at times that rare but oh so important of things, genuinely amusing. But most importantly I found that I was learning, and taking much more out of it than I ever had at college.

This post turned into something of a tribute up there. I think I'll leave it like that, only adding sincere thanks to Professor Bailyn, should he stumble his way here one day after Googling his own name or something. I thoroughly enjoyed your lectures, and greatly look forward to going into even greater depth when I get to university myself.

Ah look, we're back on topic.  From the first lecture, he started talking about these fables of science, and as I am ever one to seek the truth of things, I quickly jumped on the idea to seek the truth behind the stories, to compare and contrast. This will just be one area of this new, mildly more structured blog. I shall be posting the first fable not long after I post this. See you there.

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Radioactivity: the Discovery of the Nucleus

Today's picture heavy topic is Radioactivity: the Discovery of the Nucleus.

See, the thing is, until relatively recently, we didn't really know what we were made of. Some philosophical ideas had been thrown around for millennia that if you keep halving something that you would eventually get to a point where the cheese could no longer be halved. This tiny bit of something was referred to as "Indivisible", or ἄτομος (átomos). This was known as Atomism. The origin of this thought is widely credited to Democritus and Leucippus.

However people still believed that we were made up of the classical elements, and while such a theory is still prevalent in modern popular media, most college textbooks tend to prefer teaching the periodic table. This was due to the foundations laid by 17th century "natural philosopher" Robert Boyle with Corpuscularianism, similar to atomism, except "corpuscles" could in principle be divided. While he didn't create the idea, Robert Boyle argued in 1661 that matter was composed of various combinations of different "corpuscles" or atoms, rather than the classical elements of air, earth, fire, water and dragon.

Things didn't really progress for a while after, Corpuscuthingy being the prevalent thought of the time, until the science of chemistry was developed. In 1789, French nobleman and scientific researcher Antoine Lavoisier discovered the law of conservation of mass and defined an element as a basic substance that could not be further broken down by the methods of chemistry. Later, in 1805, discovered the John Dalton proposed that each element consists of atoms of a single, unique type, and that these atoms can join together to form chemical compounds, prompting him to become thought of as the originator of modern atomic theory. Further lines of reasoning were made by one Johann Josef Loschmid, who in a scientific landmark, worked out the size of molecules in air, and botanist Robert Brown, father of what has come to be known as Brownian motion.

In 1869, building upon earlier discoveries by such scientists as Lavoisier, Dmitri Mendeleev published the first functional periodic table. The table itself is a visual representation of the periodic law, which states that certain chemical properties of elements repeat periodically when arranged by atomic number.

Now bear with me, if you haven't left already, because here is where we finally near the content of the A2 syllabus (assuming you haven't found the last 4 paragraphs as fascinating as I have). In 1897, the electron was discovered by J. J. Thomson while pissing about with cathode rays. In doing so, he discovered that they were a component part of every atom, thus overturning the then prevalent belief that atoms are indivisible. Thomson postulated that atoms were therefore made up of the negatively charged electrons distributed, possibly in rings around a uniform sea of balancing positive charge. Thus was created one of my least liked scientific names, the Plum Pudding Model.

Douse it in brandy and set it alight, then get back to me.

Thus it was that in 1909, under the direction of Ernest Rutherford, Hans Geiger and Ernest Marsden bombarded gold foil sheets with α rays, then known to be positively charged helium atoms. Lets take a more detailed look at that. What Geiger and Marsden used was an evacuated metal box, containing an alpha source lined up with a gold foil, and a scintillator (A zinc sulphide screen that emitted light when hit by an alpha particle). What was observed was that most particles travelled straight ahead with little to no deflection. 1 in 2000 were deflected however, and very occasionally, 1 in 10 000 would be deflected at a greater angle that 90°. Some would even bounce right back to the source, an action that would be impossible for a diffuse cloud of positive charges, as Thomson had suggested. It was, in Rutherford's words "as incredible as if you fired a 15 inch naval shell at tissue paper and it came back." to give you an idea of just how surprising this was.

It would have to be at least triple ply

From this, Rutherford interpreted the results as suggesting that the positive charge of a heavy gold atom and most of its mass was concentrated in a nucleus at the centre of the atom. This was the creation of the Rutherford model. He went on to use Coulombs law of force and Newton's laws of motion to explain his results, and through the use of different metals in the same experiment he worked out that the magnitude of the charge of a nucleus was +Ze, where e was the charge of an electron, and Z was the atomic number of the element.



So there we have it. The history of the discovery of the nucleus. I could go on to the size and density, but that's decidedly mathsy, and while I love maths, it doesn't translate very well into the historical documentary format I have going here, and I fear I would end up breaking into degree level stuff, which I just do not need distracting me right now.

At any rate, I hope you enjoyed it. It has probably helped me, if not you, so at least there's that.

It is highly likely that this won't be a daily thing as it is entirely likely that I will be a) busy b) doing other things and more likely c) procrastinating.

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