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Chapter 1: Astrophysics

Quantum vs. Classical Analysis

Dear Dr. SETI:
Is the classical description of the electromagnetic wave vaild in the case of microwave SETI? In particular, is it correct to treat an incoming carrier as a classical stable wave?

Dan (via email)

The Doctor Responds:
Dan, I think your underlying question here is whether SETI signals fall into the quantum or the classical realm. The answer requires some analysis. Here is my approach:

At the 21 cm neutral hydrogen line, frequency is 1420 MHz, so energy (from h * nu) is 9.4 e -26 joules/photon. Let's call it ~ 1 e -25 joules/photon for simplicity. [A]

The flux density necessary to exceed the detector threshold of our Project Argus stations (from various articles on the SETI League website) is on the order of 1 e -23 J/s/m^2. [B]

The capture area of the typical Project Argus antenna is roughly 10 m^2. [C]

Thus, the receiver sensitivity is [C] * [B] ~ 1 e -22 J/s. [D]

The photon rate at threshold is thus [D] / [A] ~ 10^3 photons/sec. We typically integrate for tens of seconds, so our threshold is defined by a signal in excess of 10^4 photons. Without quantifying it further, this would appear to be very much a classical, not a quantum, event.

If I repeat the above analysis for a signal received at Arecibo, where system sensitivity is four orders of magnitude greater, but capture area is also four orders of magnitude greater, I get exactly the same result (threshold of ~10^4 photons)! (This is to be expected, because our Project Argus receiver noise temperature, bin width and integration times are not all that different from Arecibo's. Where their receivers excel is in processing a much larger number of simultaneous bins.)

I conclude from the above that classical analysis is always appropriate to the SETI enterprise, at the signal levels which we anticipate. Actually, that's a relief. If quantum analysis prevailed, then intelligent extraterrestrials would simultaneously exist and not exist, at probabilities p and q, respectively (where p+q=1), which we would then be forced to calculate!

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