Bohr and the breakaway from classical mechanics

May 20, 2013

One hundred years ago, Niels Bohr developed the Bohr model of the atom, where electrons go around a nucleus at the center like planets in the Solar System. The model and its implications brought a lot of clarity to the field of physics at a time when physicists didn’t know what was inside an atom, and how that influenced the things around it. For his work, Bohr was awarded the physics Nobel Prize in 1922.

The Bohr model marked a transition from the world of Isaac Newton’s classical mechanics, where gravity was the dominant force and values like mass and velocity were accurately measurable, to that of quantum mechanics, where objects were too small to be seen even with powerful instruments and their exact position didn’t matter.

Even though modern quantum mechanics is still under development, its origins can be traced to humanity’s first thinking of energy as being quantized and not randomly strewn about in nature, and the Bohr model was an important part of this thinking.

The Bohr model

According to the Dane, electrons orbiting the nucleus at different distances were at different energies, and an electron inside an atom – any atom – could only have specific energies. Thus, electrons could ascend or descend through these orbits by gaining or losing a certain quantum of energy, respectively. By allowing for such transitions, the model acknowledged a more discrete energy conservation policy in physics, and used it to explain many aspects of chemistry and chemical reactions.

Unfortunately, this model couldn’t evolve continuously to become its modern equivalent because it could properly explain only the hydrogen atom, and it couldn’t account for the Zeeman effect.

What is the Zeeman effect? When an electron jumps from a higher to a lower energy-level, it loses some energy. This can be charted using a “map” of energies like the electromagnetic spectrum, showing if the energy has been lost as infrared, UV, visible, radio, etc., radiation. In 1896, Dutch physicist Pieter Zeeman found that this map could be distorted when the energy was emitted in the presence of a magnetic field, leading to the effect named after him.

It was only in 1925 that the cause of this behavior was found (by Wolfgang Pauli, George Uhlenbeck and Samuel Goudsmit), attributed to a property of electrons called spin.

The Bohr model couldn’t explain spin or its effects. It wasn’t discarded for this shortcoming, however, because it had succeeded in explaining a lot more, such as the emission of light in lasers, an application developed on the basis of Bohr’s theories and still in use today.

The model was also important for being a tangible breakaway from the principles of classical mechanics, which were useless at explaining quantum mechanical effects in atoms. Physicists recognized this and insisted on building on what they had.

A way ahead

To this end, a German named Arnold Sommerfeld provided a generalization of Bohr’s model – a correction – to let it explain the Zeeman effect in ionized helium (which is a hydrogen atom with one proton and one neutron more).

In 1924, Louis de Broglie introduced particle-wave duality into quantum mechanics, invoking that matter at its simplest could be both particulate and wave-like. As such, he was able to verify Bohr’s model mathematically from a waves’ perspective. Before him, in 1905, Albert Einstein had postulated the existence of light-particles called photons but couldn’t explain how they could be related to heat waves emanating from a gas, a problem he solved using de Broglie’s logic.

All these developments reinforced the apparent validity of Bohr’s model. Simultaneously, new discoveries were emerging that continuously challenged its authority (and classical mechanics’, too): molecular rotation, ground-state energy, Heisenberg’s uncertainty principle, Bose-Einstein statistics, etc. One option was to fall back to classical mechanics and rework quantum theory thereon. Another was to keep moving ahead in search of a solution.

However, this decision didn’t have to be taken because the field of physics itself had started to move ahead in different ways, ways which would become ultimately unified.

Leaps of faith

Between 1900 and 1925, there were a handful of people responsible for opening this floodgate to tide over the centuries old Newtonian laws. Perhaps the last among them was Niels Bohr; the first was Max Planck, who originated quantum theory when he was working on making light bulbs glow brighter. He found that the smallest bits of energy to be found in nature weren’t random, but actually came in specific amounts that he called quanta.

It is notable that when either of these men began working on their respective contributions to quantum mechanics, they took a leap of faith that couldn’t be spanned by purely scientific reasoning, as is the dominant process today, but by faith in philosophical reasoning and, simply, hope.

For example, Planck wasn’t fond of a class of mechanics he used to establish quantum mechanics. When asked about it, he said it was an “act of despair”, that he was “ready to sacrifice any of [his] previous convictions about physics”. Bohr, on the other hand, had relied on the intuitive philosophy of correspondence to conceive of his model. In fact, even before he had received his Nobel in 1922, Bohr had begun to deviate from his most eminent finding because it disagreed with what he thought were more important, and to be preserved, foundational ideas.

It was also through this philosophy of correspondence that the many theories were able to be unified over the course of time. According to it, a new theory should replicate the results of an older, well-established one in the domain where it worked.

Coming a full circle

Since humankind’s investigation into the nature of physics has proceeded from the large to the small, new attempts to investigate from the small to the large were likely to run into old theories. And when multiple new quantum theories were found to replicate the results of one classical theory, they could be translated between each other by corresponding through the old theory (thus the name).

Because the Bohr model could successfully explain how and why energy was emitted by electrons jumping orbits in the hydrogen atom, it had a domain of applicability. So, it couldn’t be entirely wrong and would have to correspond in some way with another, possibly more successful, theory.

Earlier, in 1924, de Broglie’s formulation was suffering from its own inability to explain certain wave-like phenomena in particulate matter. Then, in 1926, Erwin Schrodinger built on it and, like Sommerfeld did with Bohr’s ideas, generalized them so that they could apply in experimental quantum mechanics. The end result was the famous Schrodinger’s equation.

The Sommerfeld-Bohr theory corresponds with the equation, and this is where it comes “full circle”. After the equation became well known, the Bohr model was finally understood as being a semi-classical approximation of the Schrodinger equation. In other words, the model represented some of the simplest corrections to be made to classical mechanics for it to become quantum in any way.

An ingenious span

After this, the Bohr model was, rather became, a fully integrable part of the foundational ancestry of modern quantum mechanics. While its significance in the field today is great yet still one of many like it, by itself it had a special place in history: a bridge, between the older classical thinking and the newer quantum thinking.

Even philosophically speaking, Niels Bohr and his pathbreaking work were important because they planted the seeds of ingenuity in our minds, and led us to think outside of convention.

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This article, as written by me, originally appeared in The Copernican science blog on May 19, 2013.

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The Last Temptation

May 4, 2013

Today, I bought The Last Temptation by Nikos Kazantzakis. When I handed the Rs. 450 it cost over at the counter, it was a significant moment for me because for the last three years, after my reading habit had fallen off but before I had realized that it had, I was rejecting books that “wouldn’t appeal to the man I wanted to become”.

I wouldn’t read books that had strong religious elements (because I wanted to be an atheist), that hadn’t good reviews (because I wanted to spend time “well”), that attended to morals and values I considered irrelevant, that hosted plots drawing upon cultural memories that were simply American or simply European but surely not global, etc. I would find the smallest of excuses to avoid masterpieces.

At the same time, I would read other books – especially non-fiction and works of fantasy fiction. To this day, I don’t know whence that part of me arose that judged literary agency before it was agent, but I do know it turned me into this pontificator who thought he’d read enough books to start judging others without having to read them. A part of me has liked to think nobody can do that. And by buying a copy of The Last Temptation (and intending to read it), I think I am out of mine.

Of course, I’m also assuming the solution is something so simple…

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Choices.

May 2, 2013

The Verge paid Paul Miller to stay away from the internet for a year.

paul_miller_verge

We have this urge to think of the internet as something that wasn’t produced by human agency, like an alien sewerage network whose filth has infected us and our lives to the point of disease. If someone has problems and they tell you about it, don’t tell me you haven’t thought about blaming the internet. I have, too. We think it is a constantly refilled dump that spills over onto our computer screens (while also hypocritically engaging in the rhetoric of how many opportunities “the social media” hold). And then, we realize that the internet is one massive improbably impressionable relay of emotions, propped up on infrastructure that simplifies access a hundredfold. There’s nothing leaving it behind will do to you because it’s always been your choice whether or not to access it.

In fact, that’s what you rediscover.

(Hat-tip to Dhiya Kuriakose)

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Which way does antimatter swing?

May 1, 2013

In our universe, matter is king: it makes up everything. Its constituents are incredibly tiny particles – smaller than even the protons and neutrons they constitute – and they work together with nature’s forces to make up… everything.

There was also another form of particle once, called antimatter. It is extinct today, but when the universe was born 13.82 billion years ago, there were equal amounts of both kinds.

Nobody really knows where all the antimatter disappeared to or how, but they are looking. Some others, however, are asking another question: did antimatter, while it lasted, fall downward or upward in response to gravity?

Joel Fajans, a professor at the University of California, Berkeley, is one of the physicists doing the asking. “It is the general consensus that the interaction of matter with antimatter is the same as gravitational interaction of matter,” he told this correspondent.

But he wants to be sure, because what he finds could revolutionize the world of physics. Over the years, studying particles and their antimatter counterparts has revealed most of what we know today about the universe. In the future, physicists will explore their minuscule world, called the quantum world, further to see if answers to some unsolved problems are found. If, somewhere, an anomaly is spotted, it could pave the way for new explanations to take over.

“Much of our basic understanding of the evolution of the early universe might change. Concepts like dark energy and dark matter might have be to revised,” Fajans said.

Along with his colleague Jonathan Wurtele, Fajans will work with the ALPHA experiment at CERN to run an elegant experiment that could directly reveal gravity’s effect on antimatter. ALPHA stands for Anti-hydrogen Laser Physics Apparatus.

We know gravity acts on a ball by watching it fall when dropped. On Earth, the ball will fall toward the source of the gravitational pull, a direction called ‘down’. Fajans and Wurtele will study if down is in the same place for antimatter as for matter.

An instrument at CERN called the anti-proton decelerator (AD) synthesizes the antimatter counterpart of protons for study in the lab at a low energy. Fajans and co. will then use the ALPHA experiment’s setup to guide them into the presence of anti-electrons derived from another source using carefully directed magnetic fields.

When an anti-proton and an anti-electron come close enough, their charges will trap each other to form an anti-hydrogen atom.

Because antimatter and matter annihilate each other in a flash of energy, they couldn’t be let near each other during the experiment. Instead, the team used strong magnetic fields to form a force-field around the antimatter, “bottling” it in space.

Once this was done, the experiment was ready to go. Like fingers holding a ball unclench, the magnetic fields were turned off – but not instantaneously. They were allowed to go from ‘on’ to ‘off’ over 30 milliseconds. In this period, the magnetic force wears off and lets gravitational force take its place.

And in this state, Fajans and his team studied which way the little things moved: up or down.

The results

The first set of results from the experiment have allowed no firm conclusions to be drawn. Why? Fajans answered, “Relatively speaking, gravity has little effect on the energetic anti-atoms. They are already moving so fast that they are barely affected by the gravitational forces.” According to Wurtele, about 411 out 434 anti-atoms in the trap were so energetic that the way they escaped from the trap couldn’t be attributed to gravity’s pull or push on them.

Among them, they observed roughly equal numbers of anti-atoms to falling out at the bottom of the trap as at the top (and sides, for that matter.)

They shared this data with their ALPHA colleagues and two people from the University of California, lecturer Andrew Charman and postdoc Andre Zhmoginov. They ran statistical tests to separate results due to gravity from results due to the magnetic field. Again, much statistical uncertainty remained.

The team has no reason to give up, though. For now, they know that gravity would have to be 100 times stronger than it is for them to see any of its effects on anti-hydrogen atoms. They have a lower limit.

Moreover, the ALPHA experiment is also undergoing upgrades to become ALPHA-2. With this avatar, Fajans’s team also hopes to incorporate laser-cooling, a method of further slowing the anti-atoms, so that the effects of gravity are enhanced. Michael Doser, however, is cautious.

The future

As a physicist working with antimatter at CERN, Doser says, “I would be surprised if laser cooling of antihydrogen atoms, something that hasn’t been attempted to date, would turn out to be straightforward.” The challenge lies in bringing the systematics down to the point at which one can trust that any observation would be due to gravity, rather than due to the magnetic trap or the detectors being used.

Fajans and co. also plan to turn off the magnets more slowly in the future to enhance the effects of gravity on the anti-atom trajectories. “We hope to be able to definitively answer the question of whether or not antimatter falls down or up with these improvements,” Fajans concluded.

Like its larger sibling, the Large Hadron Collider, the AD is also undergoing maintenance and repair in 2013, so until the next batch of anti-protons are available in mid-2014, Fajans and Wurtele will be running tests at their university, checking if their experiment can be improved in any way.

They will also be taking heart from there being two other experiments at CERN that can verify their results if they come up with something anomalous, two experiments working with antimatter and gravity. They are the Anti-matter Experiment: Gravity, Interferometry, Spectrocopy (AEGIS), for which Doser is the spokesperson, and the Gravitational Behaviour of Anti-hydrogen at Rest (GBAR).

Together, they carry the potential benefit of an independent cross-check between techniques and results. “This is less important in case no difference to the behaviour of normal matter is found,” Doser said, “but would be crucial in the contrary case. With three experiments chasing this up, the coming years look to be interesting!”

–

This post, as written by me, originally appeared in The Copernican science blog at The Hindu on May 1, 2013.

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The pain is gone.

April 28, 2013

Reading some pages of fiction touched off old memories that I’d forgotten existed, bringing back to life words and, with them, sensations. Words were between words, ideas between ideas, color underneath hue.

Earlier, I wrote not to remember or document, I wrote because I knew of no other way to digest the world; when I wrote, I grew up. Every phrase I pushed back into the inspiration whence it had come, like a bullet pressed back into the wound, I’d bleed, but the blood would be blood, just there, undigested like a colored liquid I could see, feel it crawling, but not speak about. So I wrote relentlessly, good or bad, profound or – as often was the case – meaningless.

And then I’d read myself, I’d grow up just a little, and there’d be a little more to think about life. I’m not much of a traveller, a mover even, so over time, what I wrote about would have become mundane, featureless, like a barren tract of land that lay rasping, unable to breathe air and already alien to water because it had eaten and suckled on itself, if not for books. I grew up on the minutes of lives very different from my own – or whatever lay beneath all the pages of my ink – and soon couldn’t think for myself without even the gentlest consideration of another character’s opinion.

As the years passed, I began to frighten me, I was not comfortable with the decisions I made for myself. It wasn’t that I feared that I’d be the only one to blame; in fact, that thought had never struck. No, it was simply the lack of awareness of the self, a full man beneath the patina of literature, of scientific intellect and philosophical leanings, built upon all the uncertainties and failures that the litterateur above had thwarted. A part of me had gambled me away for knowledge of the desires of other men and women, while another waited, rather cowered, in its weakening shadow.

Finally, one day, the world arrived, and robbed me away: from books, from stories, from oh-so-important The Others. What was left of me emerged, looking upon the world as a continuous litany of disappointment, the pain and the shock of humiliation – much of it in my own eyes – still evident, and took its first few steps. It tottered. It fell. It stood up, and it fell again. When it learned to stand up and straight, it refused to fall ever again.

The child was man, the writer was gone, the learner was robbed, and the world was upon me, smothering me, it smothers me still… and then I found books once more. I long to return to my shell but the emergence seems irreversible. Now, when I look upon the words, I see words: I see that they are red, viscous, flowing only with steep gradient, still and even tending to crenellate. I know that it is blood, but the nerves are deadened. The pain is gone. It is difficult to grow up when the pain is gone.

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Where’s all the antimatter? New CERN results show the way.

April 27, 2013

If you look outside your window at the clouds, the stars, the planets, all that you will see is made of matter. However, when the universe was born, there were equal amounts of matter and antimatter. So where has all the antimatter gone?

The answer, if one is found, will be at the Large Hadron Collider (LHC), the world’s most powerful particle physics experiment, now taking a breather while engineers refit it to make it even more powerful by 2015. Then, it will be able to spot tinier, much more shortlived particles than the Higgs boson, which itself is notoriously shortlived.

While it ran from 2008 to early 2013, the LHC was incredibly prolific. It smashed together billions of protons in each experiment at speeds close to light’s, breaking them open. Physicists hoped the things that’d tumble out might show why the universe has come to prefer matter over antimatter.

In fact, from 2013 to 2015, physicists will be occupied gleaning meaningful results from each of these experiments because they simply didn’t have enough time to sift through all of them while the machine was running.

They will present their results as papers in scientific journals. Each paper will will be the product of analysis conducted on experimental data corresponding to some experiment, each with some energy, some luminosity, and other such experimental parameters central to experimental physics.

One such paper was submitted to a journal on April 23, 2013, titled ‘First observation of CP violation in the decays of B_s mesons‘. According to this paper, its corresponding experiment was conducted in 2011, when the LHC was smashing away at 7 TeV centre-of-mass (c.o.m) collision energy. This is the energy at the point inside the LHC circuit where two bunches of protons collide.

The paper also notes that the LHCb detector was used to track the results of the collision. The LHCb is one of seven detectors situated on the LHC’s ring. It has been engineered to study a particle known as the beauty quark, which is more than 4.2 times heavier than a proton, and lasts for about one-hundred-trillionth of a second before breaking down into lighter particles, a process mediated by some of nature’s four fundamental forces.

The beauty is one of six kinds of quarks, and together with other equally minuscule particles called bosons and leptons, they all make up everything in the universe: from entire galaxies to individual atoms.

For example, for as long as it lives, the beauty quark can team up with another quark or antiquark, the antimatter counterpart, to form particles called mesons. Generally, mesons are particles composed of one quark and one antiquark.

Why don’t the quark and antiquark meet and annihilate each other in a flash of energy? Because they’re not of the same type. If a quark of one type and an antiquark of another type meet, they don’t annihilate.

The B_s meson that the April 23 paper talks about is a meson composed of one beauty antiquark and one strange quark. Thus the notation ‘B_s’: A B-meson with an s component. This meson violates a law of the universe physicists long though unbreakable, called the charge-conjugation/parity (CP) invariance. It states that if you took a particle, inverted its charge (‘+’ to ‘-’ or ‘-’ to ‘+’), and then interchanged its left and right, its behaviour shouldn’t change in a universe that conserved charge and parity.

Physicists, however, found in the 2011 LHCb data that the B_s meson was flouting the CP invariance rule. Because of the beauty antiquark’s and strange quark’s short lifetimes, the B_s meson only lasted for so long before breaking down into lighter particles, in this case called kaons and pions.

When physicists calculated the kaons‘s and pions‘s charges and compared it to the B_s meson’s, they added up. However, when they calculated the kaons‘s and pions‘s left- and right-handednesses, i.e. parities, in terms of which direction they were spinning in, they found an imbalance.

A force, called the weak force, was pushing a particle to spin one way instead of the other about 27 per cent of the time. According to the physicists’ paper, this result has been reached with a confidence-level of more than 5-sigma. This means that some reading in the data would disagree with their conclusion not more than 0.00001 per cent of the time, sufficient to claim direct evidence.

Of course, this wouldn’t be the first time evidence of CP violation in B-mesons had been spotted. On 17 May, 2010, B-mesons composed of a beauty antiquark and a down quark were shown shown to decay at a much slower rate than B-antimesons of the same composition, in the process outlasting them. However, this is the first time evidence of this violation has been found in B_s mesons, a particle that has been called “bizarre”.

While this flies in the face of a natural, intuitive understanding of our universe, it is a happy conclusion because it could explain the aberration that is antimatter’s absence, one that isn’t explained by a theory in physics called the Standard Model.

Here was something in the universe that was showing some sort of a preference, ready to break the symmetry and uniformity of laws that pervade the space-time continuum.

Physicists know that the weak force, one of the fundamental forces of nature like gravity is, is the culprit. It has a preference for acting on left-handed particles and right-handed antiparticles. When such a particle shows itself, the weak force offers to mediate its breakdown into lighter particles, in the process resulting in a preference for one set of products over another.

But in order to fully establish the link between matter’s domination and the weak force’s role in it, physicists have to first figure out why the weak force has such biased preferences.

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This post originally appeared in The Copernican science blog at The Hindu on April 25, 2013.

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The wayward and cowardly introspector

April 14, 2013


thinker_monkey

No water and power at home today, so I wish you a horrible Tamil New Year’s Day, too. With nothing much to do – and the sun beating down upon Chennai at an unwavering 33° C that, in the company of still airs and 80% humidity, feels simply unlivable in – I sat around almost all day and thought about my life. Yes, unlivable-in conditions are always a good time to think about life.

For the last three weeks, the science editor at The Hindu, the man who becomes my boss every Wednesday, has been getting irritated at me and with good reason: I haven’t written anything for the science page. In fact, my only contribution to this page that comes out every Thursday has been the correction of a few spelling mistakes.

I’m not going to go on about not finding stories that suit my style or some shit like that. I haven’t been writing because I haven’t been looking for stories, and I haven’t been writing because, somehow, I haven’t been able to write. Yes, writers’ block (I’ve always doubted the validity of this excuse – sure, writers claim to experience it all the time, but what are the symptoms? I’m actually surprised the condition’s immense subjectivity hasn’t seen itself forced into nonexistence).

Why haven’t I been looking for stories? Two reasons. 1) I’m not able to ‘care about the world’ in that ‘direction’, and 2) Some other stuff came my way that seemed quite exciting. This isn’t to say writing stories for The Hindu isn’t exciting: I get such a kick out of seeing my name in one of the most respected newspapers in India.

You see, my responsibilities at The Hindu include (but are not limited to) writing for the science page once a week, writing a fortnightly column for Education Plus, concocting a weekly science quiz for the In School edition, handling The Hindu Blogs - that means ensuring our bloggers are happy and motivated, the content always meets the high standards we’ve come to set, the blogs section of the site is doing well in terms of hits and user engagement, and bringing in more bloggers into the fray – working with visualizations, writing that occasional OpEd, and helping out with the tech. side of things – editorially or managerially.

So not writing for the science page doesn’t really leave me in the lurch. I can’t just sit idle.

The writers’ block, I must admit, is just me losing interest, probably because I cycle my attention to focus on different things periodically over time.

Through this introspection, I’ve realized that I’m not interested in being a journalist. I’ve just been wayward in life, not paying much attention to what I’ve been or not been interested in, while following these simple rules which The Hindu has found a way to use:

  1. Don’t give up… easily.
  2. Always contribute.
  3. Take initiative.

The pro is that, even while working with a national daily, I’ve worked in a variety of environments that any other pukka journalist might not have had the opportunity to. The con is that I can’t think of anything I’m specialized to do.

Well, there’s blogging. I can’t really put my finger on why but I love blogging. I love writing – good writing, especially (I only recently found a mentor who could really help me improve my narratives) – and I love creating such writing about different things in my life, and I love enabling other people to do the same thing.

But the buck stops there.

There’s another route I’ve often considered – academics, research, philosophy, the like – but I’ve been repeatedly convinced by a friend that if I really want to make a difference, I should consider journalism to be a better option than sitting at a desk and writing about metaphysical stuff. Right now, I’m considering academics all over again. Maybe an hour from now that friend will turn up and tell me why I’m thinking wrong.

But by then, all this wonderment will have festered into one giant carbuncle of self-doubt and, eventually, that ultimate question: What if my interests and strengths don’t coincide with the activities that are capable of making a difference in this world? Or is the pursuit of individual interests the biggest difference anyone can make?

OK, I know what I need. I need the guts to be able to answer these questions myself.

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The creative process must not be transcendental.

April 14, 2013

During a conversation with an emotionally intense and literarily prolific friend earlier this evening, the friend said many of the greatest poets had led doomed lives; doomed in the sense that they’d all suffered great misfortune – emotionally at least – and sorrow and loss. There were enough examples, too: Plath, Woolf, Hughes, Hemingway, Sexton, Haggard, going so far back as Lucanus himself. On second thought, that’s not really surprising because the greatest writers, in my opinion, are simply the greatest articulators of the human condition, however jaded or otherwise.

However, this friend also said that those poets had been recklessly extravagant with their emotional investments on purpose. That they’d deliberately led lives of misery, and that that’s where they drew their literary inspiration from. This seems an awfully distressing proposition: That you’d have to give up the right to live happily in order to be a great poet. The other problem I have with it is if a poet’s living tragic times and then writing great poetry, then the poet is simply a creative chronicler, not a poet at all.

It was a difference of opinion that the friend and I couldn’t reconcile over. While poetry may be one of the greatest forms of human expression, its pinnacle cannot be founded on human misery. Its production cannot be honed at the price of happiness… can it? I understand that these are hollow questions to ask because I’m not going to get an answer to them anytime soon (More importantly, I don’t know any poets to ask what I think must be these intimate questions).

However, to think one has expressed oneself well not by displaying commendable prowess with the tool of expression (i.e., language), not by displaying tremendous insight into the human condition and its trappings, but simply by forcing oneself to live through what I can only describe as emotional trauma is experiential writing at best, historiography at worst. It’s a convenient route through which one accumulates pain to the point of forcing it to transcend one’s existence. I would imagine poetry – or any other art form for that matter – requires effort toward its creation, not simply suffering and then release. There must be room for the aesthete, too.

I’m not securing a case for ‘ars gratia artis‘ either because I’m not discussing the utilitarian or moral function of art, which is the product. I’m simply hoping to establish that the creative process must not be transcendental, while even the product may be. In other words, art has to be humanist – constituted by human agency – in order to be art (Also, my friend, I think Plath would be really disappointed if you’re suggesting she intended to kill herself to be a good poet).

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