Have a causally consistent new year

… so what? Another year, another orbit of the earth. What’s the big deal, you say?

Well! I have some New Year’s news for you. Firstly, did you know that this year we get an extra second? To deal with this I suggest counting like a computer scientist; …3, 2, 1, 0! Happy New Year!

This year will, apparently, be the International Year of Astronomy! Georgia at Earth & Sky Science has found a great way to celebrate: 365 days of Astronomy Podcasts.

If that’s not enough, why not follow your lightcone this year? I found a great site that provides an RSS feed of astronomical bodies you (yes you!) could possibly have influenced since your birth.

… what’s a lightcone, you ask?

A lightcone is the 4-D surface in space and time that a flash of light forms as it travels away from its origin. The name is actually a bit misleading. It’s less of a cone, and more of a hyper-cone; that is a cone in four dimensions. Imagine a flash of light. As it moves forward in time the light will move outwards in all directions. At any point in time the light will be confined to the area of a sphere. As time progresses, the sphere will grow in size at a constant rate. If we think of time as another dimension, and tried to draw a 4-D graph of the flash, it would be a hyper-cone.

If you are still confused, a good way to begin thinking about this is to imagine a very small circle lying flat on the ground. Now, imagine it growing and as it grows you move it upwards. Every time the circle grows one centimeter in radius, it moves one centimeter higher up. This traces out the 3-D cone you know and love. The upward direction represents time and the other directions represent a 2-D space. To generalize to a 3-D space with time, you change the idea of a growing circle to a growing sphere. Et voila: a lightcone.

… ok, so what’s so special about a lightcone, you ask?

Since a lightcone is the boundary on which a flash of light travels, and nothing can travel faster than light, the lightcone also marks the boundary of influence of a certain action. Let’s say, for example, you sneezed. Achoo. At some other time, in some other place, let’s say a book fell over. Could your sneeze have possibly caused the book to fall over? What you could do is mark two points on a graph; one representing the time and place of your sneeze and the other representing the time and place of the falling book. You could draw a lightcone originating at the sneeze point. If the other point is outside this lightcone then it is physically impossible for your sneeze to have caused the book to fall over.

You could also do the same for your birth. Draw a cone originating from earth at your birthday. Now draw points for all the stars in the sky at time: today. Any points inside your lightcone could have been influenced by your birth. The word “could” is in italics because it’s really saying: “sure, the laws of special relativity don’t disagree with you… but… there’s more to cause and effect than lightcones”. Still, it’s a fun way to learn about astronomy!

So this year be aware of your lightcone and keep track of the people and events inside it. The range of influence of your actions is probably a lot more vast than you originally thought…

Measuring the speed of light with chocolate and a microwave oven

Here’s a great excuse to eat a lot of chocolate in the name of science.

First of all, you need to understand that microwaves are just electromagnetic waves with a certain frequency and wavelength just like visible light. Wavelength is the length between consecutive peaks of the wave. It’s a very intuitive name. You can see it labeled in the picture to the right as the Greek letter “lambda” (λ). Since waves propagate (move), we can also define a quantity called the frequency. Frequency is the number of peaks of a wave that pass a certain fixed point per second. Wavelength is a measure of distance, and frequency is a measure of one divided by time. So to find the speed (“c“) of the wave, you just need to multiply these two quantities together:

c := speed = (distance) x (1/time) = (frequency) x (wavelength)

…but why the chocolate and the microwave, you ask?

What you need to do is use a microwave oven and a piece of chocolate to measure the frequency and wavelength of microwaves. Then you can find the speed of light! Fortunately, microwaves usually have the operating frequency written on the back. Check the back of your microwave. Mine says the frequency is 2450 MHz ( = 2,450,000,000/1 second).

Now that we have the frequency, all we need is the wavelength; this is where the chocolate comes in handy… You might have a microwave with a spinning dish inside. You can probably guess what that’s for. It’s to help heat things up evenly (like stirring a pot of soup on the stove). Whereas on a stove the heat is concentrated on the bottom of a pot, the energy (and thus heat) that microwaves give to food is concentrated at the peaks of the microwaves (which are standing waves in a microwave oven). If we take out the rotating dish then we can find these peaks, measure the distance between them, and find the wavelength. So we just need to heat the chocolate up a bit, find some soft spots (where the peaks of the microwave standing wave are) and measure the distance between them with a ruler.

Here’s what you’ll need:

• Large chocolate bar (bigger than 5 inches)
• Ruler (to measure distances)
• Microwave oven (with rotating dish removed)
• Coffee (optional… it goes well with chocolate)

Place the chocolate bar (unwrapped) in the microwave oven and heat it up (without moving it) until you can see soft spots forming. If I were to hazard a guess for the timing, I’d say heat about thirty seconds… but that’s a guess. It really depends how powerful your microwave oven is.

When you have at least two soft spots forming in the chocolate, take it out and try to measure the distance between them with a ruler. (I had to prod the chocolate lightly with a spoon to find the soft spots). My chocolate didn’t turn out very nicely, but I was able to make a very rough measurement of about 4.5 inches between the centers of the soft spots. Edit: when I made this measurement I forgot that I was measuring peaks of a standing wave which are half the wavelength of the microwave. So really, you should find the distance between the soft spots and multiply by 2 to get the wavelength. Thanks, Lord Axil. Somehow I must have missed a soft spot when measuring, which automatically corrected this factor of two.

Now we can use the wonders of Google to do the calculations for us. I can just type the following right in Google and it will calculate the speed in the proper units: “2450MHz*4.5inches“.

Google says:

(2450 megahertz) * 4.5 inches = 280 035 000 m / s

…but how close are we to the real answer, you ask?

We can check our answer with Google again. Just type “c” into google and it will give you the speed of light!

Google says:

the speed of light = 299 792 458 m / s

For a measurement made with a ruler and a chocolate bar, it’s not too far off. It works!

But don’t take my word for it, listen to this amateur scientist explain the experiment.