### Why SETI is a waste of time – take 2

**Monday, August 29th, 2005** at **10:12 pm** by **Wally**

Remember SETI – the Search for Extra-Terrestrial Intelligence?

Here is reason #2 that it is a waste of time (based on physics):

**Radio Frequencies and Power and all that**

There are 2 basic law of nature – which cannot be changed. These are

1. When you transmit radio frequencies, the received power level falls with distance squared.

2. All technology used to receive radio signals is imperfect, and this manifests (at the very least) as noise.

**Taking the first point.**

If you transmit a signal with a given power, then when you receive that signal from a distance of 1 metre you will receive a different power. The difference is due to the types of antennas you use, and the distance. Using special antennas helps – but you can’t get out more than you put in (if that were true then perpetual motion machines would also work, really well!).

Lets assume you transmit X, and receive Y, where Y less than X.

Mathematically, Y = c X / (d ^ 2)

Where c = a constant (less than 1), and d = distance (in metres).

Now, increase the distance to 2 metres. You will receive a power less than Y, and it should be about 1/4 as much. Increase to 4 metres, you get 1/16 as much received power and so on.

So… Assume that the little green men are transmitting the sort of powers that we transmit for radio or TV transmissions – maybe a few thousand watts, or a few tens of thousands.

Then take into account the vast distances, it does not take much to work out that the power we COULD receive (if everything worked perfectly) is very very small.

Mathematically, lets assume an alien transmits 10,000 Watts, and that there are no losses, and they are 100 light years away (which is pretty close really).

The most wildly optimistic receive power is 10000 / [( 100 light years, in metres) ^2] Watts (because this does not take into account the frequency dependant effects).

(1 light year = distance for light to travel in a year = 3 x 10^8 [metres/sec] x 365 [hours / day] x 24 [hours / day] x 60 [hours / minute] x 60 [minutes / sec] = 6.46 x 10^15 metres)

So, the best possible receive power is roughly 10000 / (9 x 10^35) = 10^-32 watts.

In engineering speak, that’s -290 dBm.

This is a number so mind bogglingly small that it needs a damn good receiver to pick it up.

**Taking the second point**

When we build a receiver for a radio signal, it has noise. We have all heard noise – it’s that hissing “static” sound in a radio that’s not tuned on. This is an extreme example.

If we ignore all other sources of noise and concentrate only on **Thermal noise** (which is often a big contributor anyhow), the amount of thermal noise is given by:

N = kTB (in Watts)

Where:

N = noise power,

k = Boltzmann’s constant, 1.38 x 10^-23

T = temperature in Kelvins

B = Bandwidth in Hertz

The important point about noise is that it is additive – so it is added to the signal we receive, and to detect a signal we need lots of it, so the amount of noise added needs to be small compared to the signal.

If we fix the bandwidth at 1 Hz (which is impossibly small) we have a noise power at room temperature (approx 290 Kelvin) of 4 x 10^-21 Watts (or -174 dBm in engineering speak).

It does not take much to see that if the noise power in a ridiculously small bandwidth is MUCH LARGER than the best possible receive signal power, then we are not going to detect a signal.

We can make things better by reducing the temperature of the receiver. Let’s cool the receiver with something jolly flash, and get temperature down to (say) 20 Kelvins – which is damn cold.

This gives a noise power of 2.76 x 10^-22 watts, or -185 dBm. Still does not cut it. And that is in a 1 Hz bandwidth – still impossibly small.

The only way that we can see the transmissions of the little green men is if they have a DAMN BIG antenna with a DAMN BIG transmitter, POINTED RIGHT AT US.

And even then we would have to be looking at the same frequency, and at the same time.

Those who wish to lecture me about antenna gains and correct my maths with a more exact RF link budget – go right ahead – it will get closer but the point still stands – both sides need antenna gains of > 50 dB to come even remotely close. We can be pretty sure that the little green men will not have a focussed antenna pointing at us, so there won’t be 50 dB of antenna gain on their side. We might have it on ours – maybe even more. Still does not come close.

So… waste of time. It’s trying to break the laws of physics.

Wally,

Isn’t noise chaotic? And wouldnt signals be somewhat less random? doesnt that offer the seti team some chance of detecting something if it exist?

Dunc.