Over the last few weeks there was a claim from Russia that a possible alien signal was detected, this was later downplayed as potential terrestial noise. Other articles have appeared to continue the theme surrounding the 'Zoo hypothesis' which contends that humans are kept in the dark by unknown alien parties. To me, this latter position sounds more like Cold War thinking, rather than an advanced civilization.
Personally, I think it is a case that our radio engineering sucks and we're still using formulas from classical physics, rather than quantum mechanics.
Most modern radio communications still rely on theoretical work perform during WWII:
Claude Shannon's development of information theory during World War II provided the next big step in understanding how much information could be reliably communicated through noisy channels. Building on Hartley's foundation, Shannon's noisy channel coding theorem (1948) describes the maximum possible efficiency of error-correcting methods versus levels of noise interference and data corruption. The proof of the theorem shows that a randomly constructed error-correcting code is essentially as good as the best possible code; the theorem is proved through the statistics of such random codes.
Let's examine a quick worked example of capacity on a noisy channel:
Shannon's Theorem gives an upper bound to the capacity of a link, in bits per second (bps), as a function of the available bandwidth and the signal-to-noise ratio of the link.
The Theorem can be stated as:
C = B * log2(1+ S/N)
where C is the achievable channel capacity, B is the bandwidth of the line, S is the average signal power and N is the average noise power.
The signal-to-noise ratio (S/N) is usually expressed in decibels (dB) given by the formula:
10 * log10(S/N) so for example a signal-to-noise ratio of 1000 is commonly expressed as
10 * log10(1000) = 30 dB.
Anyone that has ever done any form of radio engineering or courses on data transmission theory, has had at some point to learn these formulas. The above formula defines the baud rate, or bits per second, that can be achieved. In short, the great the signal-to-noise ratio, the more bandwidth a radio channel can provide. To many, these are seen as hard limits and indeed used daily to plan radio installations all over the world.
This said, most are not aware that thanks to modern quantum mechanics, we can blast past these limits and Shannon's work does not quite apply in certain scenarios. Let's delve into some new physics and explain this.
A very simple relationship is that the lower the energy of a photon, the more of them it takes to generate 1W of power. This is shown in the math below:
E = hc/λ
E = Energy in Joules
h = Planck's constant
c = speed of light
λ = wavelength
λ 1Hz = 299,790,000m
λ 2Hz = 149,900,000m
λ 10Hz = 29,979,000m
E = ((6.626068 * 10e-34) * (299792458)) / wavelength
E = 1.986445212595144e-25 / wavelength
E 1Hz = 6.6261223276131425331065078888555e-34
E 2Hz = 1.3251802619046991327551701134089e-33
E 10Hz = 6.6261223276131425331065078888555e-33
number of photons per second = 1 Watt (or 1 J/s) / energy of a photon (J)
1Hz = 1.5091782954755973367955496869703e+33
2Hz = 7.54614318328803631827789112635e+32
10Hz = 1.5091782954755973367955496869703e+32
The total theoretical capacity for a binary 1W signal, over 1 second, is:
1Hz = 1.5091782954755973367955496869703e+33 bits
2Hz = 7.54614318328803631827789112635e+32 bits
10Hz = 1.5091782954755973367955496869703e+32 bits
Ignoring all of Shannon's work, what we can see is the exact opposite of what many hold true. Rather than bandwidth increasing as we move up the spectrum, it is actually decreasing. Why is this? Well, this is mainly to do with analogue vs. digital modulation schemes. In analogue we are concerned with waves/waveforms, with digital we are mostly concerned with symbol representation.
If we look carefully, we can see the more photons we have, the more symbols we can represent for a given power level. Obviously two key factors apply here, photon generation and detection above thermal noise.
Ignoring photon generation for a second, we can observe that to detect photons well below the noise floor, all we need to do is entangle them, allowing us to pick them out of the random photons flying about. There are a number of additional measures that are taken care of by protocols, but this, in theory, this can allow for Yottabit transmission rates at 1Hz using 1W of power.
Given this, I feel that a more plausible answer as to why we hear nothing out in space is because they use point-to-point power transmissions, rather than high power omni-directional transmissions, for a wide variety of reasons from health to the massive cost savings on pure raw bandwidth.
Surely it would be dumb to employ any other technology for very long.