In a previous post, I calculated how much energy it would take to travel to Proxima Centauri, the nearest star outside of our own solar system, within a reasonable amount of time. The results were rather discouraging; barring any monumental revolutions in physics, energy considerations alone suggest that interstellar travel might be downright impossible.

So let’s set aside thoughts of space travel and consider a far more modest project: merely broadcasting a *signal* to the stars (in hopes of contacting intelligent alien life, assuming there is any). Surely, simply sending a signal would be much easier than transporting a massive spaceship over such a long distance. So let’s see what it would take.

First, we need to define the problem.

Suppose our goal is just to send out a signal that is detectable on Proxima Centauri, our nearest neighbor. And suppose that we have at our disposal a transmitter that sends a uniformly intense signal out in all directions. The question we wish to answer is how much energy it would take to generate such a signal.

To complete the setup of the problem, there are two things that we need to specify:

- What exactly does it mean for a signal to be “detectable”?
- What is the nature of this signal? (Visible light? Radio waves? X-rays?)

Let’s tackle the first question first, and let’s be optimistic about aliens’ signal-detection capabilities. We’ll assume that aliens can detect our signal if it consists of at least one photon (a particle of light) per second flowing through one square meter of area when it reaches the aliens’ location. This is actually an über-weak signal, but as I said, we’re going to be optimistic here.

The second question is important because the amount of energy carried by each photon depends on the nature of the signal. If it’s a radio wave, which is low-frequency, then the amount of energy required is relatively low. Microwaves, visible light, and X-rays have higher frequencies and would require more energy. To keep the requirements low, let’s assume our signal consists of radio waves; and to keep the numbers simple, let’s suppose these waves have a wavelength of one meter.

We now have enough information to solve the problem.

Since the signal is being sent out uniformly in all directions, it is essentially a sphere that’s expanding at the speed of light, with the Earth at its center. Assuming the photons are uniformly distributed over this sphere, and keeping in mind that we want there to be one photon per square meter, we simply need to calculate the surface area (in square meters) of this expanding sphere when it arrives at the destination, Proxima Centauri.

Well, Proxima Centauri is 4.24 light-years away from us, so when the signal arrives there, the radius of the sphere is 4.24 light-years. Calling this distance R, the formula for the surface area of a sphere tells us that a total of 4*pi*R^2 square meters must be covered. And if we want one photon to pass through each of those square meters per second, that’s also the number of photons per second that our transmitter must send out. (Note that we have to convert R to meters.)

That’s 2×10^34 photons.

The amount of energy per photon is E = hc/L, where h is Planck’s constant and L is the wavelength of the radio waves (and c, of course, is the speed of light). So the total amount of energy (per second) is just hc/L times the number of photons, which works out to be 4 billion joules. Since that’s the amount of energy *per second*, the amount of *power* is 4 billion Watts.

All right. So what?

Well, that’s about the output of a large power plant, which is a lot of power to put into one signal. And that signal will thin out to just one tiny photon per square meter per second by the time it reaches our nearest neighbor in the universe. In reality, it would have virtually no chance of being detected, even if someone were looking for it with highly advanced technology. Farther away, the signal would be even weaker.

So the sad truth is that even if we devoted a huge amount of energy into attempts to contact extraterrestrial life forms, our signals would dissipate to undetectable levels long before they reached any of the distant planets that might harbor life. We can conclude from this analysis that a radio transmitter that sends a signal in all directions just won’t cut it.

There are other possibilities, though.