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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.

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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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Intuitively, there is an optimal mass for a ball being thrown. If it’s too heavy then we won’t be able to give it a large initial speed. Too light, and it will be slowed down very quickly by air resistance. A shot is too heavy, a tennis ball too light.

To calculate the optimal mass for a projectile, we need to have a model for how a thrower accelerates the ball before release. I will make what is perhaps the simplest assumption: the force applied by the throwers arm and the distance over which that force is applied are held constant. This is equivalent to assuming that the thrower will impart a fixed amount of kinetic energy (K) to the ball. Then, the initial speed (v) of the ball varies with the mass (m) as,

v = \sqrt{\frac{2 K}{m}}

K will be fixed using the fiducial case of a cricket ball thrown with initial velocity of 120, 140 and 160 km/h. As before, the launch angle is chosen to maximise the range of the throw for a 1.8m tall thrower.

The plot shows that, as expected, there is a mass which maximises the range of the throw. It is quite close to the actual mass of a cricket ball (0.16 kg, dashed vertical line) and a baseball (0.145 kg), which is a satisfying result. The optimal mass increases slightly with the force applied by the thrower (i.e. the fiducial initial velocity v_0).

Next time: how much easier is it to hit a six (or a home run) at higher altitudes?

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More fun with wind-resistance! (The cricket season starts for me tomorrow. Cracking.)

Last time, I showed a few trajectories of cricket balls (or baseballs) thrown in the presence of wind-resistance. I noted that I had chosen the angle of the throw in order to maximise the range of the throw. This optimal angle changes as the throw speed changes, as shown below.

The first thing to note in that the optimal throwing angle in the absence of wind-resistance is not 45 degrees, because the ball is released from 1.8m above the ground. (It would be 45 degrees if thrown from ground level). The angle is significantly less than 45 degrees at low speeds – maximum range requires a balance between vertical velocity (giving you more air-time) and horizontal velocity (giving you more range). The height of the thrower gives the ball extra air-time for free, so the thrower should use a flatter launch angle when throwing speed is small.

In the presence of wind-resistance, the optimal throwing angle drops below 45 degrees for very fast throws. The second, descending part of the balls trajectory will be slower and steeper than it would be in the absence of wind-resistance, so our thrower should opt for a flatter trajectory to take advantage of the higher velocity of the ball during its ascent.

In short, about 40 degrees should do it. Next time – will making the cricket ball heavier help?

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Fun with Wind-Resistance (Part 1)

It’s finally happened. After a decade of dealing with frictionless slopes, massless strings, perfect vacuums and other spherical cows, I’m ready to complicate my model. What follows is a simple model for wind resistance, as outlined in University Physics by Young and Freedman. We’ll then have a look at the effect of air resistance on throwing a cricket ball (or baseball, if you must.)

In the absence of wind resistance, the equation of motion for a projectile is quite simple:

a_x = 0

a_y = -g

In the x-direction (horizontally), the ball moves with whatever horizontal velocity the thrower  gave it to start with. In the y-direction (vertically), the ball is pulled downwards, its vertical velocity changing at the constant rate of 9.8 m/s/s.

Wind resistance adds an extra force, one that pushes in the opposite direction to the way the ball is going. The magnitude of the force (for sufficiently large Reynolds number) is

F_D = \frac{1}{2}\rho v^2 C_d A

where $latex v$ is the speed of the ball, \rho is the density of air (1.2 kg/m^3), A is the cross sectional area of the ball and C_d is a dimensionless factor called the drag coefficient.

Because the drag force increases with velocity, a falling ball will accelerate until it reaches terminal velocity, where the drag force balances gravity. Thereafter, the ball falls with a constant velocity. The terminal velocity is given by:

v_{t} = \sqrt{\frac{2mg}{\rho A C_d}}

In practice, we use this formula in a different way. The terminal velocity is measurable, so we can use it to constrain the drag coefficient C_d. E.g. for a cricket ball, the terminal velocity is 123 km/h.

We now have all the pieces we need. The equation of motion is not solvable analytically, but is easily handled by any good numerical ODE solver. I’ll be using those of Matlab.

Let’s start with a few trajectories. I’m assuming that the thrower releases the ball from 1.8m.

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Let’s begin by quoting from Radford Neal:

There is a large literature on the Anthropic Principle, much of it too confused to address.

I’ve previously quoted John Leslie:

The ways in which ‘anthropic’ reasoning can be misunderstood form a long and dreary list.

My goal in this post is to go back to the original sources to try to understand the anthropic principle.

Carter’s WAP

Let’s start with the definitions given by Brandon Carter in the original anthropic principle paper:

Weak Anthropic Principle (WAP): We must be prepared to take account of the fact that our location in the universe is necessarily privileged to the extent of being compatible with our existence as observers.

Carter’s illustration of WAP is the key to understanding what he means. Carter considers the following coincidence: (more…)

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I remember a technology TV show in the mid 90’s showing a roller coaster simulator ride. The audience is shown a simulation or video of the view out the front of a roller coaster, and the seats jostle and tilt in concert with the footage. I was only 11, but I concluded that it was the coolest thing ever.

Why they are almost convincing

There is a good physics reason why these rides are almost convincing. Galilean relativity says that inertial reference frames are indistinguishable using local experiments. In layman’s terms, if you are in an enclosed plane traveling in a straight line at a constant speed, then there is nothing you can do inside the cabin to work out how fast you are travelling1. The plane could be stationary or it could be doing a thousand miles per hour, and you won’t notice any difference between walking up the aisle and down the aisle.

In a car, we gauge speed by looking out the window and watching the scenery fly past. Ride simulators can simulate a fast moving roller coaster by showing a simulation of scenery going past. They also simulate the bumps and shunts by jostling your seat – the faster your car is going, the more you will feel the small deviations from uniform motion due to potholes.

I’ve been on a few of these rides, and I’m not fully sucked in. Speed is fine, bumps are fine, but the most exciting part of a real roller coaster ride is the “stomach in your throat” feeling as you go over a crest, or being thrown to one side as you take a corner at speed. Unlike speed, acceleration can be measured locally, so it can’t be simulated with a video and a shaky chair.

How to make them fully convincing

There is a way to simulate acceleration. Einstein’s equivalence principle roughly states that freely falling is locally indistinguishable from zero gravity. We can illustrate this point with a thought experiment. Suppose you wake up in an elevator which is freely falling (i.e. ignore wind resistance etc). There is nothing you can do inside the elevator to determine whether you are freely falling, or whether someone has turned off gravity2. If you want to know what it would be like if there were no gravity, then go jump off a cliff (in your mind, of course). (more…)

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