Archive for the ‘Astronomy’ Category

Having read a few good books on Aristotelian and scholastic (meta)physics (and, thanks to Scholastic Metaphysics: A Contemporary Introduction by Edward Feser, maybe starting to get a grip on what a formal cause is supposed to be), I’d had a few idle thoughts about what a mathematical formalisation of Aristotle’s physics would look like. Aristotle, and his colleagues in the Middle Ages, distinguished between pure mathematics, which studies abstractions, and natural philosophy, which tries to understand the physical world. The problem child for this scheme was astronomy, which studied the natural world and yet did so in terms mathematical, quantitative abstractions. Astronomy was thus categorised as a middle science.

It was Descartes (as best I can tell) who first championed the audacious idea that all of physics could be as mathematical as astronomy. Newtonian mechanics gives us the first complete example of such a physical theory, mathematical from its very foundations.

It is no coincidence that these two names – Descartes and Newton – are pivotal in the development of mathematical physics. They were not just physicists. Descartes pioneered analytic geometry, and Newton developed calculus. In trying to understand the physics of motion, it is (for a modern physicist!) difficult to know where to start if you don’t know about using variables to represent space and time, and rates of change of position. (Although, just to put a spanner in this oversimplified account, Newton largely relied on clever arguments from geometry rather than calculus in developing his theory of mechanics.)

But what if we used the resources of modern mathematics to analyse Aristotelian physics? Having had this idle thought, I was very pleased to see someone else do all the hard work. Carlo Rovelli’s “Aristotle’s Physics: a Physicist’s Look” is great! Here’s the abstract:

I show that Aristotelian physics is a correct and non-intuitive approximation of Newtonian physics in the suitable domain (motion in fluids), in the same technical sense in which Newton theory is an approximation of Einstein’s theory. Aristotelian physics lasted long not because it became dogma, but because it is a very good empirically grounded theory.

Rovelli summarises the qualitative principles of Aristotelian physics as follows:

  1. There are two kinds of motion: violent (or unnatural) motion, and,
  2. Natural motion.
  3. Once the effect of the agent causing a violent motion is exhausted, the violent motion ceases.
  4. The natural motion of the Ether in the Heavens is circular around the centre.
  5. The natural motion of Earth, Water, Air and Fire is vertical, directed towards the natural place of the substance.
  6. Heavier objects fall faster: their natural motion downwards happens faster.
  7. The same object falls faster in a less dense medium.
  8. The speed v of fall is proportional to the weight W of the body and inversely proportional to the density ρ of the medium. (Technically, as a power law.)
  9. The shape of the body accounts for their moving faster or slower.
  10. In a vacuum with vanishing density a heavy body would fall with infinite velocity.
  11. From what has been said it is evident that void does not exist.

Rovelli’s claim is that “Aristotle’s physics is the correct approximation of Newtonian physics in a particular domain, which happens to be the domain where we, humanity, conduct our business. This domain is formed by objects in a spherically symmetric gravitational field (that of the Earth) immersed in a fluid (air or water) and the main celestial bodies visible from Earth.” The total force on such objects is given by:

Total Force = gravity + buoyancy + viscosity (fluid resistance) + external force

Within this Newtonian model, we understand Aristotle’s principles as follows.

  1. Violent motion is when there is an external force.
  2. Natural motion is when there is no external force.
  3. Because of viscosity, the effect of violent motion decays away in a finite time.
  4. The motion of planets under gravity (buoyancy and viscosity being negligible), viewed from a rotating Earth, can be described using circular orbits. Remember that, within the observational limits of the ancient Greeks, Ptolemy’s model works!
  5. A buoyant body, initially at rest and immersed in a fluid, “will immediately start moving up or down, according to whether its density is higher or lower than the density of the fluid in which it is immersed. Therefore Earth will move down in any case. Water will move down in Air. Air will move up in water.” And so on. “Furthermore, if a body is immersed in a substance of the same kind, as Water in Water, then it can stay at rest: it is at its natural place.”
  6. The terminal velocity of a buoyant body falling in a viscous fluid increases with its mass. Thus, ignoring the transient period of acceleration when gravity is dominant, heavy objects fall faster.
  7. The terminal velocity of an object (ignoring buoyancy) is inversely proportional to the (square root) of the density of the medium.
  8. Combining the two points above gives Aristotle’s law. In fact, the terminal velocity is proportional to the square root of the weight divided by the density. “What Aristotle does not have is only the square root … which would have been hard for him to capture given the primitive mathematical tools he was using. His factual statements are all correct.”
  9. The constant in the law in h) depends on the shape of the object.
  10. Somewhat surprisingly, this is a correct inference from the Newtonian model of Aristotle’s physics, in that as the density approaches zero, the terminal velocity approaches infinity. This doesn’t happen, of course, and identifies an unrealistic assumption: that the gravitational field is everywhere uniform. In reality, the falling object would eventually hit the mass originating the attraction.
  11. Following the conclusion of the model in j.), and supposing that infinite velocities are impossible, one must conclude that the vacuum is a physical impossibility. This is an interesting lesson in extrapolating physical theories beyond their domain of validity.

Aristotle’s physics is obviously not perfect – Rovelli lists all the important failings – but it does a very good job in the right regime, summarising the more complete physical model of Newton.

A few of Rovelli’s conclusions are worth quoting.

“Aristotelian physics is often presented as the dogma that slowed the development of science. I think that this is very incorrect. The scientists after Aristotle had no hesitation in modifying, violating, or ignoring Aristotle’s physics. … In the Middle Ages the physics of Aristotle was discussed and modified repeatedly, but it took Copernicus, Galileo, Kepler and Newton to find a more powerful theory. … The reason Aristotelian physics lasted so long is not because it became dogma: it is because it is a very good theory. … With all its limitations, it is great theoretical physics.”

“The bad reputation of Aristotle’s physics is undeserved, and leads to widespread ignorance: think for a moment, do you really believe that bodies of different weight fall at the same speed? Why don’t you just try: take a coin and piece of paper and let them fall. Do they fall at the same speed? Aristotle never claimed that bodies fall at different speed “if we take away the air”. He was interested in the speed of real bodies falling in our real world, where air or water is present. It is curious to read everywhere “Why didn’t Aristotle do the actual experiment?”. I would retort: “Those writing this, why don’t they do the actual experiment?”. They would find Aristotle right.”

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A favourite XKCD:

Made out of Meat

Here’s a few idle, Friday afternoon thoughts. I study distant galaxies. I use mathematical models of the laws of nature (and a supercomputer) to try to predict the properties of light emitted by and scattered through swirling vortices of matter, each containing a thousand trillion trillion trillion tons of stars, gas and dark matter, almost a trillion trillion kilometers away. My discipline – cosmology – has taken as its object of study the universe as a whole. And we’re doing pretty well, thanks for asking. I’d like to think that I am an evidence collecting, theory discovering, model investigating, equation solving (with a little help from my computer) machine.

And then I hear a talk from a biologist. I am reminded that I’m a fighting, fleeing, feeding, and reproducing machine. The lump of stuff in my head was produced by causes that “see” survival and reproduction. My brain is the control centre of a biological organism, and there seems to be precious little overlap between survival, reproduction and astrophysical ability. (Unless my astrophysical brain has made me so attractive to the ladies that it significantly increases my chances of reproduction. I’ll ask my wife.) An accurate mental picture of the world, formed using mostly reliable senses and the ability to reason logically, creatively and flexibly, seems useful to survival. But to use a brain to do cosmology? Really? (If you haven’t read Terry Bisson’s wonderful short essay “They’re made out of meat“, then do it now: “Thinking meat! You’re asking me to believe in thinking meat!”.)

A parable. Suppose I call Toyota customer services.

Me: Hi there. I own a 1993 Toyota Camry. I have a question.

Toyota: Certainly, sir. Is the car running well, getting you from A to B in comfort?

Me: Sure. It’s doing all that nicely. I was thinking about using it to drive to the moon.

Toyota: … Right … Wouldn’t recommend that, Mr Barnes. No … uh … not really in the user manual, I’m afraid. Not what it’s made for.

Suppose I find a customer support label on the back of my brain.

Me: Hi there. I own and operate one of your brains. I have a question.

Support: Certainly, sir. Is it operating your body, correctly? Are you getting enough food? Have you found a mate?

Me: Sure. It’s doing all that nicely. I was thinking about using it to do theoretical physics, discover the fundamental laws of the universe and use them to understand the structure and evolution of the universe and all its contents.

Support: … Right … Wouldn’t recommend that, Mr Barnes. No … uh … not really in the user manual, I’m afraid. Not what it’s made for.

Let’s be clear about the point I’m making here. I don’t doubt that physicists in general and cosmologists in particular have discovered true facts about the universe. It’s just a tad amazing that we can do that sort of things with our brains. (We use computers and telescopes as well, of course, but they too are the products of human brains). To extend the analogy, it’s as if I find myself standing on the moon, wondering how I got there. And as I look around, all I can see is a 1993 Toyota Camry. It’s not that I doubt where I am; I’m wondering how I got here in that! I’m not asking: how do I know that our investigation of the universe is successful? I’m asking: why is our investigation of the universe successful? How does fighting/fleeing/feeding/reproducing machine manage to do theoretical physics?

Perhaps the boring answer is the right one: we do it bit by bit. If we view science as extended and refined common sense, then maybe we can understand how a brain “made for” understanding local terrestrial environments is able to understand the universe. We don’t directly grasp the universe, of course. We rely on mental pictures and analogies. Mathematical models of the universe are perhaps analogies with equations. Having a mental picture of the world is useful. Just add curiosity and get practicing.

It seems like the same problem arises for mathematics – how does a brain manage to investigate such abstract ideas as those of pure mathematics? The same answer suggests itself: abstract thinking is useful. Just add curiosity and get practicing.

The universe is easy

We seem to need another ingredient in this explanation. That a brain can do theoretical physics and cosmology suggests not only that it is a remarkably adaptable, programmable thing, but also that the universe is an easier problem than we might have expected. A great example of this is the so-called cosmological principle. (I discuss this in more detail in my Australian Physics article here.)

That the universe is rationally analysable at all, that there is order and reason waiting for us in the mathematical structure of the universe, is a remarkable fact. The intellectual problem we are presented with in nature is, in a very real and precise sense, solvable.  It is one thing that the universe exemplifies such beautiful mathematics as Lagrangian dynamics; it is another, a fortiori, that the Lagrangians that describe our universe display numerous and deep symmetries. The universe is a complicated place, and the mathematics that describes it must be complicated at some level. The remarkable thing is that the complication is on top; there is simplicity underneath. To be more precise, the laws of nature are simple, their solutions can be complicated. Newton’s law of gravitation is simple, but for even three bodies, its solution cannot be written down analytically.

In physics’s search for the ultimate laws of nature, many physicists wouldn’t accept a proposed fundamental theory unless it were simple, elegant, and beautiful. Paul Dirac went so far as to say that “it is more important to have beauty in one’s equations than to have them fit experiment”. It follows that physics cannot explain why the laws of nature are simple, elegant, and beautiful. Now there’s a thought for the weekend.

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It’s been a while, but I’ve finally gotten around to jotting down a few thoughts about the Sean Carroll vs. William Lane Craig debate. I previewed the debate here (part one, two, three, four). I thoroughly enjoyed the debate. Future posts will discuss a few of the philosophical questions raised by the debate, but I’ll briefly discuss some of the science in this point. (I didn’t manage to record my talk a few weeks ago, but this post summarises it.)

Firstly, I want to refer you to the much greater expertise of Aron Wall of UC Santa Barbara. I’ll list them all because they’re great.

(I’m on the “astrophysics” end of cosmology. The beginning of the universe probes the “particle and plasma and quantum gravity and beyond” end of cosmology. I know the field, but not as well as someone like Wall or Carroll.)

No one expects the beginning of the universe!

Regarding the scientific question of the beginning of the universe, here is how I see the state of play. Cosmologists don’t try to put a beginning into their models. For the longest time, even theists who believed that the universe had a beginning acknowledged that the universe shows no sign of such a beginning. We see cycles in nature – the stars go round, the sun goes round, the planets go round, the seasons go around, generations come and go. “There is nothing new under the sun”, says the Teacher in Ecclesiastes. Aristotle argued that the universe is eternal. Aquinas argued that we cannot know that the world had a beginning from the appearance of the universe, but only by revelation.

So when a cosmic beginning first raised its head in cosmology, it was a shock to the system. Interestingly, theists didn’t immediately jump on the beginning as an argument for God. Lemaître, one of the fathers of the Big Bang theory and a priest, said:

“As far as I can see, such a theory [big bang] remains entirely outside any metaphysical or religious question.”

In 1951, Pope Pius XII declared that Lemaître’s theory provided a scientific validation for existence of God and Catholicism. However, Lemaître resented the Pope’s proclamation. He persuaded the Pope to stop making proclamations about cosmology.

The philosophical defence of the argument from the beginning of the universe to God (the Kalam cosmological argument) starts essentially with Craig himself in 1979, half a century after the Big Bang theory is born.

In fact, the more immediate response came from atheist cosmologists, who were keen to remove the beginning. Fred Hoyle devised the steady state theory to try to remove the beginning from cosmology, noting that:

“… big bang theory requires a recent origin of the Universe that openly invites the concept of creation”. His steady-state theory was attacked “because we were touching on issues that threatened the theological culture on which western civilisation was founded.” (quoted in Holder).

Tipping the Scales

But what of the beginning in the Big Bang model? Singularities in general relativity weren’t taken seriously at first. Einstein never believed in the singularities in black holes. Singularities were believed to be the result of an unphysical assumption of perfect spherical symmetry. In Newtonian gravity, a perfectly spherical, pressure-free static sphere will collapse to a singularity of infinite density. However, this is avoided by the slightest perturbation of the sphere, or by the presence of pressure. A realistic Newtonian ball of gas won’t form a singularity, and the same was assumed of Einstein’s theory of gravity (General Relativity).

The next 80 years of cosmology sees the scales tipping back and forth, for and against the beginning. (more…)

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I’ve been a bit quiet around here, lately. Travel is my excuse. I’m currently in Cambridge, collaborating with a few colleagues on a project. I’ll be back in Sydney next week, so if you’re near Epping on Friday 4th July 2014, why not come along to hear me speak at the Astronomical Society of NSW:

“What Happened at the Big Bang?”

Friday 4th July 2014 – 8:00pm
Topic: What happened at the Big Bang?
Speaker: Dr Luke Barnes, University of Sydney
Venue: Epping Creative Centre – 26 Stanley Road, Epping

Was the big bang the beginning of the universe? Does the big bang represent the beginning of time itself? This is an age-old question, and has been remarkably informed by modern cosmology.

I will answer this question once and for all.

I will follow the theorems, evidence and hints that lead us back in time. In particular, I will discuss the expansion of the space, the physics of the very early universe, the recent BICEP2 results and cosmic inflation, the effect of quantum physics, and the reason (or one of them) why Stephen Hawking is famous.

Dr Luke A. Barnes is a postdoctoral researcher at the Sydney Institute for Astronomy. After undergraduate studies at the University of Sydney, Dr. Barnes earned a scholarship to complete a PhD at the University of Cambridge. He worked as a researcher at the Swiss Federal Institute of Technology (ETH), before returning to Sydney in 2011. He has published papers on galaxy formation and cosmology, and recently has taken an interest in the fine-tuning of the universe for intelligent life. He blogs at letterstonature.wordpress.com.

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The Conversation has published an article of mine, co-authored with Geraint Lewis, titled “Have cosmologists lost their minds in the multiverse?“. It’s a quick introduction to the multiverse in light of the recent BICEP2 results. Comments welcome!

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Front Cover of Australian PhysicsMy article “Cosmology Q & A” has been published! It appeared in the magazine Australian Physics, 51 (2014) 42-6 and is reproduced here with permission. After a brief overview of modern cosmology, it (tries to) answer the following questions:

  1. Is space expanding, or are galaxies just moving away from us?
  2. Is everything getting bigger?
  3. Ordinary matter and radiation cause the expansion of the universe to decelerate. But our universe is accelerating! How? What is the universe made of?
  4. Dark Energy? Is that like Dark Matter?
  5. How big is the universe?
  6. How big is the universe really?
  7. If the universe were finite, could I see the back of my own head?
  8. Is space expanding faster than the speed of light?
  9. Are there galaxies moving away from us at more than the speed of light?
  10. Light from distant galaxies is observed to be redshifted. Is this because the expansion of space stretches the wavelength, or because is it a Doppler shift due to the recession of the galaxy?
  11. Does the universe have zero total energy?
  12. Energy is not conserved!? Shouldn’t that send shivers up the spine of any physicist?
  13. The very universe, we are told, began in thermal equilibrium. How did equilibrium establish itself so quickly?
  14. How does the initially smooth universe we see in the CMB become today’s universe of stars and galaxies?

As before, further questions in the comments are always welcome.

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I don’t know who Rob Sheldon is, but he doesn’t know much about cosmology. He recently was quoted in this post at uncommondescent.com regarding the geometry of the universe. If I lecture cosmology this year, I’ll set this passage as an assignment: find all the mistakes. It gets more wrong than right. I have an article for “Australian Physics” on common questions about cosmology that I’ll post here once it’s out (a fortnight, maybe). In the meantime, I’ll try to clear up a few things.

The discussion of the mathematics of curvature (flat, positive, negative) is about right. It’s when he discusses the universe that things go wrong.

It takes a lot of effort to find any curvature at all, and certainly it is difficult to get good agreement between different types of measurement.

Nope. That’s why it’s called the “concordance model of cosmology” – because the different measurements converge on the same set of cosmological parameters. For example, this plot.

… a “closed” universe that collapses back down to itself …

A common error. In a matter and radiation-only universe, closed implies collapsing. A cosmological constant and/or dark energy changes this: closed vs. open no longer divides collapse vs. expand forever. Here is the plot you’ll need, from John Peacock’s marvellous Cosmological Physics.

… one would like it to have positive curvature to avoid infinities …

Flat and negatively curved universes can be finite. A flat 3-torus, for example, is finite, unbounded and has a flat geometry. Einstein’s general relativity constrains the geometry of the universe but not its topology. (more…)

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