omething finally happened that's not a war, plague, or mass slaughter: NASA
says it wants to send messages to space.
A NASA spokesman was
quoted
as saying
Logic suggests a species which has reached sufficient complexity to achieve communication through the cosmos would also very likely have attained high levels of cooperation amongst themselves and thus will know the importance of peace and collaboration.
In fact, logic suggests that there may be a very good reason why no one, as far as we know, has ever picked up any messages from extraterrestrials: they either don't exist or they know something that we don't. There's also the danger of making a galactic faux pas trying to talk to beings we know nothing about.
But first we must ask whether it's possible to send a radio message to aliens at all. We all know that data bits from Voyager 1 are now sent at fewer than 160 bits/second. What is the data rate for sending a message to the nearest star?
Basic concepts
Radio waves between one and ten GHz are thought to be optimal because, even though visible and infrared laser beams can be made much tighter, the background is much lower in the microwave region. How strong would the signal have to be?
Calculating that is easy. Most people use decibel notation to make things easier. A decibel always refers to a comparison between two different things. They're logarithmic, so we can't have a dB when one of the things is zero.
Some definitions:
dB = 10 log10(power2/power1)
dBm = 10 log10(power/1mW)
dBW = 10 log10(power/1W)
p in dBm = 10 log10(p in watts)) + 30
p in milliwatts = 10((p in dBm) / 10)
p in watts = 10((p in dBm−30) / 10)
dBm = dBW + 30
dBi = 10 log10(signal from antenna/signal from isotropic emitter)
dBd = 10 log10(signal from antenna/signal from dipole antenna)
For example, if a receiver picks picks up a signal of −100 dBm it means the signal is 1×10−10 milliwatts or 1×10−13 watts or −130 dBW.
Let's assume the following:
Antenna = Arecibo-size, 68 dBd, collecting area = 73,000 m2
Distance d = 9.46×1012 km = 1 light year
Frequency f = 1×1010 Hz = 10 GHz
Speed of light c = 299,792 km/s
Transmit power = 1×106 watts
Gain of transmitting antenna Gt = 68 dBi
Gain of receiving antenna Gr = 68 dBi
We need only two concepts to calculate the data rate: free space signal loss and the Shannon-Hartley theorem.
Free space signal loss
Free space signal loss in decibels is given by the following equation:
fspl = 20 log10(d) + 20log10(f) + 20 log10(4π/c) − gt − gr
Note the factors are 20, not 10, because the formula has a square term.
pr/pt = (4π * d * f / c)2
fspl = 10log10(pr/pt) in decibels
fspl = 10log10((4π * d * f / c)2 )
= 20log10(4π * d * f / c)
For 10 GHz, fspl over one light year is
fspl = 10log10((4π × 9.46×1012 × 1×1010 / 299792)2)
fspl = 20log10(1.57×1037)
= 371.96 dB not counting antenna gain
= 235.96 dB counting antenna gain
To overcome such an enormous signal loss we need large antennas. For transmitting, either a dish or a planar array will work. For receiving, it's much more practical to use a dish because a detector has to be cooled to liquid helium temperatures to reduce noise.
Signal
The signal is 1×106 watts or 90 dBm at 1×1010 Hz. This gives us an effective radiated power or ERP, which is the power adjusted for the directional antenna, of 6.3096×1012 watts. Correcting for the antennas, a receiver 1 light year away will get a signal of 90 − 235.96 = −145.96 dBm or 2.535×10−15 milliwatts. A receiver ten light years away will get a signal 100 times lower, or 90 − 255.96 dBm = 2.53×10−17 mW.
Noise
The thermal noise floor is −173.96 dBm/Hz at room temperature (290K) or −193.6 at 3K. The cosmic microwave background (CMB) noise in an antenna the size of Arecibo at 10 GHz is about 6.219×10−22 mW/Hz or −212 dBm/Hz. No technology, no matter how advanced, can eliminate these two factors. Let's add extra 5 dBm to allow them to decode the signal and we get −168.9 dBm or 1.288 ×10−17 mW as the lowest usable signal.
Some papers on the subject recommend using wideband microwaves because they're cheaper to transmit. Others suggest various modulation techniques, such as QPSK, to boost the data rate. But if the goal is to be detected we have to avoid fancy modulation schemes and keep the bandwidth as narrow as possible. This limits the data rate but makes it much easier to detect because the aliens can use a narrowband filter. This is why ham radio operators can transmit much greater distances by CW than by voice.
Shannon-Hartley theorem
Now we're ready to calculate the data rate, using Claude Shannon's famous formula for the capacity of a communication channel. The formula is
C = W log2(1 + S/N)
C = W log10(1 + S/N) / log102
where:
C = the channel capacity in bits/sec
S = received power
N = noise power
W = bandwidth in Hertz
So, for 1 light year we set the bandwidth to 10 Hz (we want at least one cycle per bit to avoid the need for complicated multi-level modulation schemes, which need a high S/N ratio to work):
W = 10 Hz
S signal is 2.535×10−15 milliwatts
N noise is 10 × 1.288 ×10−17 milliwatts
C = 1 × log10(1+S/N) / log10(2)
C = log10(20.68) / 0.301 = 4.37 bits/sec
Of course, there are no aliens that close. Even within ten light years there are only 20 stars. At that distance the bit rate is 0.259 bits/sec. The throughput barely increases if we narrow the bandwidth to 2 Hz (0.989 bps). At 100 light years, even at a bandwidth of 0.2 Hz, we only get 0.135 bps or one bit every 7.38 seconds. Thus, under perfect conditions, with no noise and two big antennas pointing directly toward each other (at least one of which no longer exists), and aiming at one of the twenty nearby stars, we could send one bit every 1.153 seconds.
To send an uncompressed 256×256 image at 1 bit/pixel of two humans making the “call me” gesture with one hand and holding their cell phones in the classic taking-a-selfie-in-the-mirror position with the other, we would need 65,536 bits, which would take 75,589 seconds or 21 hours. (It must be uncompressed if we assume noise in the channel and that the aliens would have no clue how to decode a JPEG from first principles.) This assumes that there is no noise other than CMB, they're using a perfect receiver, and they have a computer that can run for 21 hours without needing to download security updates and reboot, which is something we humans have yet to achieve.
If we're limited to EM radiation (instead of, say, neutrinos or gravitational waves, which pass through matter without being attenuated), the limiting factor at long distances becomes energy. One solution would be to use a giant liquid crystal to modulate the light from the Sun. It would have to be 865,000 miles in diameter, but if our sun suddenly started blinking CQ over and over in Morse code it would certainly get someone's attention.
How would extraterrestrial beings react?
Humans project their political anxieties and ambitions onto extraterrestrial beings and undoubtedly, if they existed, they'd project theirs onto us. If they're anything like us, they'd just ignore anything that conflicts with their worldview. Anything we send, even a picture, would be denied as a hoax. Indeed, they might not have a system for disseminating scientific discoveries at all. They would certainly find NASA's belief that they “know the importance of peace and collaboration” embarrassingly naive.
But it's also foolish to think they'd be anything like us. Carl Sagan was only indulging in political propagandizing when he claimed they could have destroyed themselves with nuclear weapons. True, if they had science they might practice genetic engineering on themselves to make themselves more intelligent or turned themselves into Dalek-like creatures with plungers instead of arms. But it's far more likely that any life we encounter would be like birds, reptiles, or fish: maybe intelligent in some sense, but unable or unwilling to create science or technology and utterly uninterested in communicating with us.
Considering the astronomical cost of space travel, it's even more absurd to worry about aliens coming here to collect resources or colonize us. The possibility of a plague is also extremely remote considering that they would share zero DNA with our species.
Unfortunately, the calculations here show that the probability of ever finding out by sending radio signals is vanishingly small. Indeed, given the low bit rate, many astronomers have concluded that if we want to send a message it would be more effective to tie it to an interstellar rock and throw it through their window, so to speak, instead.
apr 10 2022, 6:07 am. last updated apr 12 2022 5:15 am
