Dreamt of in Your Philosophy

This week, I got several questions from Papou about the Big Bang and thermodynamics:

Is the Universe a closed system?

In order to answer this, we need to define what is meant by a "closed system": This is where no matter or energy enters or leaves the system under consideration. That means that the Earth, which gets energy from the Sun and radiates it back into space, is not a closed system. The Universe, however, which contains all matter and energy observed, is a closed system.

A different question, which uses confusingly similar terms, is whether the Universe is open or closed in the geometric sense. This refers to what happens if you travel in a straight line: Do you eventually come back to where you started, like you would on the surface of the Earth? Due to the influence of dark energy, for our universe the answer is no, it is geometrically open, whatever Modest Mouse may tell you.

How do the Laws of Thermodynamics apply to the Big Bang Theory?

Before we dive into this, let's talk about what the laws of thermodynamics are:

1. The energy in a closed system remains constant.
2. In any process, the entropy of the system must increase or stay the same.
3. As temperature approaches absolute zero, entropy approaches a constant

These are sometimes summarized as

1. You can't win.
2. You must lose.
3. You have to play the game.

I've mentioned entropy a couple of times on this blog, each time in a slightly different context. In this case, it can be thought of as energy that can no longer be used for work. As an example, if you have a bottle of compressed air, you could use it to propel a cart or turn a pinwheel, but if everything's at the same pressure, the air won't flow. This is actually the plot of a short story I read recently called Exhalation, about robots powered by compressed gas.

The Big Bang theory states that all matter and energy in the Universe started at a single point, which expanded outward. We can check off the first law, since the theory isn't saying anything about where that point came from – The Universe started with some fixed energy, and that energy is still here, just more spread out. That last part applies to laws 2 and 3 – Spreading out means more possible states for the matter, and lower temperature. It's these laws that lead to the heat death of the Universe, which I described before.

What is the impact of the Laws of Thermodynamics on Evolution?

The laws I outlined above are sometimes used as an argument against evolution: Evolution makes things more ordered, but that violates the increasing entropy requirement. The key is that the second law doesn't say entropy everywhere increases, just that it increases in the system as a whole. It's true that a human body has less entropy than a pile of microbes of the same mass, but that skips all the entropy generated in producing a human body. For a (slightly) more detailed discussion, I found this page, written by Robert Oerter at George Mason University.

Can there ever be enough Hawking Radiation to eliminate a Black Hole?

Yes! Hawking radiation is a process by which black holes can emit particles, but according to the first law up above, that means the black hole must lose energy/mass. If this happens over enough time, or the black hole is small enough, it can eventually evaporate. When the Large Hadron Collider first started up, some people (not scientists) were afraid it would create a black hole that would swallow the Earth. Experts were confident that if it did create one of the hypothesized microscopic black holes, they would quickly evaporate under Hawking radiation.

Thanks for more great questions, Papou!

Candlemass

On a camping trip a little while ago, I was watching the wood shift in the fire, and I came up with an interesting thought experiment: If you put a candle on a scale and light it, what does the scale read over time? Obviously over a long time, the measured weight will decrease, since the candle is burning away, but for a short time after lighting, would the weight appear to go up from the mass being ejected from the candle?

The candle is throwing gasses upward at some velocity, giving them momentum. This in turn pushes the candle down with the same change in momentum, similar to how a rocket works. Change in momentum is the same as a force, and we also have gravity pushing down according to the current mass:

To calculate the momentum change, I decided to use the average speed of an ideal gas:

Where k is Boltzmann's constant, T is the temperature in Kelvin, and m is the mass of the molecule. When things burn, they typically give off two types of molecules: water, and carbon dioxide. To figure out how much, we'll need to do a bit of chemistry. Candle wax is typically a large hydrocarbon, which combines with oxygen:

For beeswax, n is 45, so since I'm a physicist, I'm going to call that big and throw out those plus-2s to say that for every 1 unit of carbon burned, there are 2 units of hydrogen and 3 of oxygen. Now we can write the total change in force as 

The Wikipedia article I linked above gives a burn rate of about 0.1 g/minute. Plugging in a couple different temperatures, we can plot this function over a few minutes:

Impressively, the candle will register a greater force on the scale for around 8 minutes! Less impressively, that extra force will be around 2 thousandths of a pound. Looks like Yankee Candle won't be starting a space program anytime soon.

The Great Mubbet Caber

I may have mentioned before that I'm a big fan of the British quiz show QI. A recent episode included a discussion of an event from the Scottish Highland Games, the caber toss. In the sport, competitors must throw what amounts to a tree trunk such that it flips end-over-end and lands pointing as straight as possible away from them. You can see a video with some examples here:

I was really curious about the physics involved in determining a successful flip. I decided to make a simplified model of the sport: The competitor holds the caber at an initial angle θ, measured from the horizontal behind them. Then they run forward up to a speed v, and stop, exerting a torque on the end of the caber. It continues forward, while beginning to spin. When one end touches the ground, it sticks, and then the initial speed and gravity determine which direction it falls.

Based on the Wikipedia article I linked above, I tried a range of different lengths (5-7.75 m), angles (45-90°), and initial velocities (1-7.5 m/s or 2-17 mph). For each case, I ran the simulation and tested whether the caber fell away, or back toward the athlete. The plots below show the results, with blue indicating success, and red failure. As the length changes, the successful ranges shift, and for the shortest cabers they can even flip twice (blue region in the upper right)!

For the longest case, I also animated the throws for the 4 corners: min/max speed and angles:

As with many of these posts, I'm not sure understanding the theory would make me any more able to compete, but I'm content to use my imagination!