How many photons are received per bit transmitted from Voyager 1?

Order-of-magnitude estimate and encoding details

• Commenters are impressed that the photons-per-bit estimate is tractable with relatively simple physics and energy arguments.
• Consensus: the back-of-envelope math looks reasonable as an order-of-magnitude estimate; antenna directionality and link budget are well-characterized.
• Several note that Voyager’s raw 160 bps stream is convolutionally encoded and later Reed–Solomon coded, with an effective symbol rate around 320 baud and useful throughput nearer 140 bps.
• For “photons per useful bit,” the 140 bps figure matters; for Shannon–Hartley capacity, the 320 Hz bandwidth should be used.

Shannon limit, noise, and how far we can communicate

• Discussion centers on when Voyager would hit the Shannon limit vs when its power fails; current expectation is that power loss is the real cutoff.
• Multiple levers are mentioned to extend range: larger or arrayed dishes, lower bitrates with stronger coding, cooler receivers, and using relays.
• Some argue theoretically there is no finite distance limit if one accepts arbitrarily low data rates and ideal coding.
• Others clarify that “Shannon limit” in practice often means the Shannon–Hartley AWGN case; more general quantum/Poisson models (Gordon–Holevo limit) can allow better performance with photon-counting and pulse-position modulation.

Photons, EM spectrum, and intuition

• Many readers are struck by how few photons per bit are received and by the idea that radio waves are just very low-frequency photons.
• There is informal explainer content on the electromagnetic spectrum, wave–particle duality, detector size, and why RF vs optical differ mainly by wavelength and materials.
• Several comments emphasize that signals can be reliably decoded “below the noise floor” via coding and long integration.

Quantum information and repetition in classical systems

• The original question is tied to illustrating how classical systems effectively use massive repetition (many photons/electrons per bit), whereas naive repetition in quantum systems often makes things worse due to measurement-induced errors.
• Commenters contrast classical bit-flip errors with quantum phase flips and describe more sophisticated quantum codes (e.g., Shor-like and surface codes) that require large physical-to-logical overhead.

Alternatives and future tech (optical links, MIMO, compressed sensing)

• There is extended discussion of optical deep-space communication: tighter beams, photon counting, and current demos (e.g., laser links from spacecraft).
• Tradeoffs: directionality vs pointing difficulty, solar background for uplink, and atmospheric issues.
• Compressed sensing is discussed as exploiting sparsity to reduce sampling rates, but not as a way to violate Shannon; it changes assumptions, not the fundamental information limits.