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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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If you’re in Sydney on Monday (18th May, 2015), then come along to The Royal pub in Darlington to see A Pint of Science! It’s an international science festival, with similar events in 9 countries. I’ll be speaking on:

Universes, one after the other)
Cosmologists are considering the idea that our universe is just one of a vast ensemble. I’ll give two reasons to take that incredulous look off your face, and two reasons to put that incredulous look right back again.

You’ll also hear “Quantum origin of galaxies, stars and life”, by Archil Kobakhidze (theoretical particle physicist), and Quantum Technologies of the Future by David Reilly (quantum physicist).

And, naturally, beer. All 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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Having had my appetite for the Middle Ages whetted by Edward Grant’s excellent book A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, I recently read Edward Feser’s Aquinas (A Beginner’s Guide). And, on the back of that, his book The Last Superstition. If I ever work out what a formal cause is, I might post a review.

In the meantime, I’ve quite enjoyed some of his blog posts about the philosophical claims of Lawrence Krauss. This is something I’ve blogged about a few times. His most recent post on Krauss contains this marvellous passage.

Krauss asserts:

“[N]othing is a physical concept because it’s the absence of something, and something is a physical concept.”

The trouble with this, of course, is that “something” is not a physical concept. “Something” is what Scholastic philosophers call a transcendental, a notion that applies to every kind of being whatsoever, whether physical or non-physical — to tables and chairs, rocks and trees, animals and people, substances and accidents, numbers, universals, and other abstract objects, souls, angels, and God. Of course, Krauss doesn’t believe in some of these things, but that’s not to the point. Whether or not numbers, universals, souls, angels or God actually exist, none of them would be physical if they existed. But each would still be a “something” if it existed. So the concept of “something” is broader than the concept “physical,” and would remain so even if it turned out that the only things that actually exist are physical.

No atheist philosopher would disagree with me about that much, because it’s really just an obvious conceptual point. But since Krauss and his fans have an extremely tenuous grasp of philosophy — or, indeed, of the obvious — I suppose it is worth adding that even if it were a matter of controversy whether “something” is a physical concept, Krauss’s “argument” here would simply have begged the question against one side of that controversy, rather than refuted it. For obviously, Krauss’s critics would not agree that “something is a physical concept.” Hence, confidently to assert this as a premise intended to convince someone who doesn’t already agree with him is just to commit a textbook fallacy of circular reasoning.

The wood floor guy analogy is pretty awesome, so be sure to have a read.

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The ABC’s opinion pages has posted my introduction to the debate between Lawrence Krauss and William Lane Craig, happening this evening at the Sydney Town Hall. The debate topic is “Why is there something rather than nothing?”. Can science answer the question? Can God? Can anyone? Read on.

(more…)

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It’s always useful to know a statistics junkie or two. Brendon is our resident Bayesian. Another colleague of mine from Zurich, Ewan Cameron, has recently started Another Astrostatistics Blog. It’s well worth a look.

I’m not a statistics expert, but I’ve had this rant in mind for a while. I’m currently at the “Feeding, Feedback, and Fireworks” conference on Hamilton Island (thanks Astropixie!). There has been some discussion of the problem of reification. In particular, Ray Norris warned that, once a phenomenon is named, we have put it in a box and it is difficult to think outside that box. For example, what was discovered in 1998 was the acceleration of the expansion of the universe. We often call it the discovery of dark energy, but this is perhaps a premature leap from observation to explanation – the acceleration could be being caused by something other than some exotic new form of matter.

There is a broader message here, which I’ll motivate with this very interesting passage from Alfred North Whitehead’s book “Science and the Modern World” (1925):

In a sense, Plato and Pythagoras stand nearer to modern physical science than does Aristotle. The former two were mathematicians, whereas Aristotle was the son of a doctor, though of course he was not thereby ignorant of mathematics. The practical counsel to be derived from Pythagoras is to measure, and thus to express quality in terms of numerically determined quantity. But the biological sciences, then and till our own time, has been overwhelmingly classificatory. Accordingly, Aristotle by his Logic throws the emphasis on classification. The popularity of Aristotelian Logic retarded the advance of physical science throughout the Middle Ages. If only the schoolmen had measured instead of classifying, how much they might have learnt!

… Classification is necessary. But unless you can progress from classification to mathematics, your reasoning will not take you very far.

A similar idea is championed by the biologist and palaeontologist Stephen Jay Gould in the essay “Why We Should Not Name Human Races – A Biological View”, which can be found in his book “Ever Since Darwin” (highly recommended). Gould first makes the point that “species” is a good classification in the animal kingdom. It represents a clear division in nature: same species = able to breed fertile offspring. However, the temptation to further divide into subspecies – or races, when the species is humans – should be resisted, since it involves classification where we should be measuring. Species have a (mostly) continuous geographic variability, and so Gould asks:

Shall we artificially partition such a dynamic and continuous pattern into distinct units with formal names? Would it not be better to map this variation objectively without imposing upon it the subjective criteria for formal subdivision that any taxonomist must use in naming subspecies?

Gould gives the example of the English sparrow, introduced to North America in the 1850s. The plot below shows the distribution of the size of male sparrows – dark regions show larger sparrows. Gould notes:

The strong relationship between large size and cold winter climates is obvious. But would we have seen it so clearly if variation had been expressed instead by a set of formal Latin names artificially dividing the continuum?

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I’m going to jump back on one of my favourite high horses. I’ve previously blogged about Lawrence Krauss and his views on the question “why is there something rather than nothing?”. I’ve just finished his book, and he appeared last night on an Australian TV show called Q&A. It was a good panel discussion, but as usual the show invites too many people and tries to discuss too much so there is always too little time. Krauss’ discussions with John Dickson were quite interesting.

I’ll be discussing the book in more detail in future, but listening to Krauss crystallised in my mind why I believe that science in principle cannot explain why anything exists.

Let me clear about one thing before I start. I say all of this as a professional scientist, as a cosmologist. I am in the same field as Krauss. This is not an antiscience rant. I am commenting on my own field.

Firstly, the question “why is there something rather than nothing?” is equivalent to the question “why does anything at all exist?”. However, Krauss et al have decided to creatively redefine nothing (with no mandate from science – more on that in a later post) so that the question becomes more like “why is there a universe rather than a quantum space time foam?”. So I’ll focus on the second formulation, since it is immune to such equivocations.

Here is my argument.
A: The state of physics at any time can be (roughly) summarised by three things.

1. A statement about what the fundamental constituents of physical reality are and what their properties are.
2. A set of mathematical equations describing how these entities change, move, interact and rearrange.
3. A compilation of experimental and observational data.

In short, the stuff, the laws and the data.

B: None of these, and no combination of these, can answer the question “why does anything at all exist?”.

C: Thus physics cannot answer the question “why does anything at all exist?”.

Let’s have a closer look at the premises. I’m echoing here the argument of David Albert in his review of Krauss’ book, which I thoroughly recommend. Albert says,

[W]hat the fundamental laws of nature are about, and all the fundamental laws of nature are about, and all there is for the fundamental laws of nature to be about, insofar as physics has ever been able to imagine, is how that elementary stuff is arranged. (more…)

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