Why science cannot explain why anything at all exists

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.

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Fun with Wind-Resistance (Part 3) – Optimal mass

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,

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 ).

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

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Fun with Wind-Resistance (Part 2) – Optimal throwing angle

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:

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

where $latex v$ is the speed of the ball, is the density of air , is the cross sectional area of the ball and 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:

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 . 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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The Traps of WAP and SAP

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:

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A Better Roller Coaster Simulator

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).

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In Defence of The Fine-Tuning of the Universe for Intelligent Life

I recently posted on Arxiv a paper titled “The Fine-Tuning of the Universe for Intelligent Life”. A slightly shortened version has been accepted for publication in Publications of the Astronomical Society of Australia. The paper is primarily a review of the scientific literature, but uses as a foil Victor Stenger’s recent book “The Fallacy of Fine-Tuning: Why the Universe Is Not Designed for Us” (FoFT). Stenger has since replied to my criticisms. The following is my reply to his reply to my article criticising his book which criticises fine-tuning. Everybody got that?

A few points before I get into details:

• There isn’t much in this post that wasn’t in my original article. I write this to summarise the important bits.
• “Barnes does not challenge my basic conclusions.” Not even close. Re-read.
• “Barnes seems to want me to reduce this to maybe 1-5 percent.” Nope. I didn’t say or imply such a figure anywhere in my article. On the contrary, the cosmological constant alone gives . The Higgs vev is fine-tuned to . The triple alpha process plausibly puts constraints of order on the fine-structure constant. The “famous fine-tuning problem” of inflation is (Turok, 2002). The fine-tuning implied by entropy is 1 in according to Penrose. For more examples, see my article. Or just pull a number out of nowhere and attribute it to me.
• “He fails to explain why my simplifications are inadequate for my purposes.” Red herring. My issue is not oversimplification. I do not criticise the level of sophistication of Stenger’s arguments (with one exception – see my discussion of entropy in cosmology below). Stenger’s arguments do not fail for a lack of technical precision. Neither does the technical level of my arguments render them “irrelevant”.

Point of View Invariance (PoVI)

A major claim of my response (Section 4.1) to FoFT is that Stenger equivocates on the terms symmetry and PoVI. They are not synonymous. For example, in Lagrangian dynamics, PoVI is a feature of the entire Lagrangian formalism and holds for any Lagrangian and any (sufficiently smooth) coordinate transformation. A symmetry is a property of a particular Lagrangian, and is associated with a particular (family of) coordinate transformation. All Lagrangians are POVI, but only certain, special Lagrangians – and thus only certain, special physical systems – are symmetric. Stenger replies:

“PoVI is a necessary principle, but it does not by itself determine all the laws of physics. There are choices of what transformations are considered and any models developed must be tested against the data. However, it is well established, and certainly not my creation, that conservation principles and much more follow from symmetry principles.”

Note how a discussion of PoVI segues into a discussion of symmetry with no attempt to justify treating the two as synonymous, or giving an argument for why one follows from the other.

Of course conservation principles follow from symmetry principles – that’s Noether’s theorem. It’s perfectly true that “if [physicists] are to maintain the notion that there is no special point in space, then they can’t suggest a model that violates momentum conservation”. The issue is not the truth of the conditional, but the necessary truth of the antecedent. Physicists are not free to propose a model which is time-translation invariant and fails to conserve energy¹. But we are free to propose a model that isn’t time-translation invariant without fear of subjectivity.

And we have! Stenger says: “But no physicist is going to propose a model that depends on his location and his point of view.” This is precisely what cosmologists have been doing since 1922. The Lagrangian that best describes the observable universe as a whole is not time-translation invariant. It’s right there in the Robertson-Walker metric: a(t). The predictions of the model depend on the time at which the universe is observed, and thus the universe does not conserve energy. Neither does it wallow in subjectivity.

Watch closely as Stenger gives the whole game away:

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James Jeans and our finite universe(?)

“Leave only three wasps alive in the whole of Europe and the air of Europe will still be more crowded with wasps than space is with stars, at any rate in those parts of the universe with which we are acquainted.”

I love a good illustration.

For whatever reason, I’m drawn to old popular-level science books. I just finished reading “The Stars in Their Courses” by James Jeans, first published in 1931. Jeans is best known in my field for the “Jeans length”. Suppose a cloud of gas is trying to collapse under its own gravity, but is being held back by gas pressure. Jeans showed that there is a critical length scale, such that if the object is smaller than the Jeans length then pressure wins and the cloud is stable, but if it is larger then gravity wins and collapse ensues.

Jeans gives an overview of all of the astronomy of his day. It’s mostly familiar material, of course; the interesting bit is the glimpse inside the mind of the great scientist. Here’s a neat illustration:

“If we could take an ordinary shilling out of our pocket, and heat it up to the temperature of the sun’s centre [40 million kelvin], its heat would shrivel up every living thing within thousands of miles of it.”

Repeating this calculation, I think Jeans is reasoning as follows. A shilling is about 5 grams of copper (specific heat capacity 0.385 J/gram/kelvin), and so at 40,000,000 K we have about J of energy. This is ‘only’ 20 kg of TNT – most bombs are at least a tonne of TNT equivalent, and they don’t do miles of damage. That much energy could raise the temperature of the surrounding air to boiling point for about a 10 metre radius. Not too promising. However, the coin will be emitting thermal radiation at x-ray wavelengths. A lethal dose of x-rays is about 5 J/kg, so our coin has enough energy to kill about 100,000 people. One must factor in the fraction of energy emitted horizontally, the fraction absorbed by biological material, the cooling of the coin, etc, but certainly it’s a very dangerous coin.

Jeans’ views on cosmology are very revealing. He is writing within 5 years of the discovery of the expansion of the universe by Lemaitre (first!) and Hubble. Jeans says:

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Book Review: The Cosmic Landscape by Leonard Susskind (Part 1)

I’m a great fan a popular science books, particularly when the topic is cosmology or fundamental physics. Susskind’s “The Cosmic Landscape” was particularly enjoyable, though I will take issue with a few things in later posts. For now, here are a few highlights:

I love a good illustration:

A rocket-propelled lemon moving away from you might have the color of an orange or even a tomato if it were going fast enough. While its moving toward you, you might mistake it for a lime.

This is simply the Doppler effect, which we’ve all observed for sound as an ambulance drives past. It works for light as well, but you have to be going close to the speed of light. Using the right formula from Einstein’s special relativity, we find that you must fire a lemon at a tenth of the speed of light to make it look red. About the same speed, but moving toward you, will make it look green.

Susskind gives an excellent account of the fine-tuning of the universe for intelligent life.

[T]he Laws of Physics may not only be variable but are almost always deadly. In a sense the laws of nature are like East Coast weather: tremendously variable, almost always awful, but on rare occasions, perfectly lovely. … One theme has threaded its way through our long and winding tour from Feynman diagrams to bubbling universes: our own universe is an extraordinary place that appears to be fantastically well designed for our own existence. This specialness is not something that we can attribute to lucky accidents, which is far too unlikely. The apparent coincidences cry out for an explanation.

In particular, he takes the discussion to the cutting edge of particle physics, discussing the gauge hierarchy problem:

Physicists puzzled for some time about why the top-quark is so heavy, but recently we have come to understand that it’s not the top-quark that is abnormal: it’s the up- and down-quarks that are absurdly light. The fact that they are roughly twenty thousand times lighter than particles like the Z-boson and the W-boson is what needs an explanation. The Standard Model has not provided one. Thus, we can ask what the world would be like is the up- and down-quarks were much heavier than they are. Once again – disaster!

… the cosmological constant problem:

Throughout the years many people, including some of the illustrious names in physics, have tried to explain why the cosmological constant is small or zero. The overwhelming consensus is that these attempts have not been successful.

… fine-tuning of cosmic inflation needed to give the universe the right amount of lumpiness:

A lumpiness of about 10^-5 is essential for life to get a start. But is it easy to arrange this amount of density contrast? The answer is most decidedly no! The various parameters governing the inflating universe must be chosen with great care in order to get the desired result.

… and even supersymmetry:

The biggest threat to life in an exactly supersymmetric universe [has to do] with chemistry. In a supersymmetric universe every fermion has a boson partner with exactly the same mass, and therein lies the trouble. The culprits are the supersymmetric partners of the electron and the photon. These two particles, called the selectron (ugh!) and the photino, conspire to destroy all ordinary atoms. … in a supersymmetric world, an outer electron can emit a photino and turn into a selectron. … That’s a big problem: the selectron, being a boson, is not blocked (by the Pauli exclusion principle) from dropping down to lower energy orbits near the nucleus. … Goodbye to the chemical properties of carbon – and every other molecule needed by life.

Susskind is also clear to distinguish between the landscape of string theory and a multiverse (or megaverse):

The two concepts – Landscape and megaverse [a.k.a. multiverse] – should not be confused. The Landscape is not a real place. Think of it as a list of all the possible designs of hypothetical universes. Each valley represents one such design. … The megaverse, by contrast, is quite real. The pocket universes that fill it are actual existing places, not hypothetical possibilities.

All in all, the Susskind’s book is highly recommended.

Part 2 of my review is here.

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Ivan Karamazov and Euclid

Peter Kreeft once commented (in a talk – sorry I can’t give a reference) that he tells his undergraduate students that “if your faith is weak and you don’t want to lose it then don’t read The Brothers Karamazov by Fyodor Dostoyevsky”. I can scarcely think of a better recommendation for a book. And as if you need more reason, observe this gem (page 274 of the Penguin paperback):

[Ivan:] … if God really exists and if he really has created the world, then, as we all know, he created it in accordance with the Euclidean geometry, and he created the human mind with the conception of only the three dimensions of space. And yet there have been and there still are mathematicians and philosophers, some of them indeed men of extraordinary genius, who doubt whether the whole universe, or, to put it more wildly, all existence was created only according to Euclidean geometry and they even dare to dream that two parallel lines which, according to Euclid can never meet on earth, may meet somewhere in infinity. I, my dear chap, have come to the conclusion that if I can’t understand even that, then how can I be expected to understand about God?

The Brothers Karamazov was published in 1880. Ivan is referring to the discovery a few decades earlier by Lobachevsky that Euclidean geometry is not unique, and thus it is an empirical matter whether or not parallel lines meet (or are unique) in our universe. This seems like a very minor loose thread in physics, and yet when Einstein pulled on it, 35 years after Ivan’s monologue, he was lead to General Relativity, arguably the greatest achievement of a single physicist since Newton. Gravity is geometry!

This quote came as quite a surprise to me. I hadn’t realised that non-Euclidean geometry had reached popular culture in the 1880′s.

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