[HN Gopher] How many photons are received per bit transmitted fr...
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       How many photons are received per bit transmitted from Voyager 1?
        
       Author : williamsmj
       Score  : 762 points
       Date   : 2024-06-03 12:07 UTC (10 hours ago)
        
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       | notorandit wrote:
       | It's really nice! Both the question and the answer!
        
       | jsjohnst wrote:
       | Didn't realize the math would be that straightforward. Is there
       | something the author isn't taking into account or is that a
       | decent plausible range?
        
         | krylon wrote:
         | I was surprised, too. Knowing little about physics, this was a
         | pleasant surprise, however.
        
         | rcxdude wrote:
         | It looks like a pretty reasonable order of magnitude estimate
         | to me. Energy arguments tend to be quite neat for that because
         | if the efficiency is at all reasonable they constrain things
         | well with fairly simple calculations. The antenna
         | directionality is also reasonably well understood and
         | characterised. The exact noise level discussed later on is
         | probably where things get a bit more uncertain (but aren't
         | directly needed to answer the question).
        
         | magicalhippo wrote:
         | One thing that seems missing to me is that while the probe
         | might send 160 bits/sec of useful data, those bits are not sent
         | directly as such[1]:
         | 
         |  _The TMU encodes the high rate data stream with a
         | convolutional code having constraint length of 7 and a symbol
         | rate equal to twice the bit rate (k=7, r=1 /2)._
         | 
         | So the effective symbol rate is 320 baud[2], and thus a factor
         | of two should be included in the calculations from what I can
         | gather.
         | 
         | Note that the error correction was changed after Jupiter to use
         | Reed-Solomon[3] (255,223) to lower the effective bit error
         | rate, so effectively I guess the data rate is more like 140
         | bps.
         | 
         | [1]:
         | https://web.archive.org/web/20130215195832/http://descanso.j...
         | 
         | [2]: https://destevez.net/2021/09/decoding-voyager-1/
         | 
         | [3]: https://destevez.net/2021/12/voyager-1-and-reed-solomon/
        
           | ooterness wrote:
           | For the "photons per bit" question, the useful throughput of
           | 140 bps is the only thing that matters.
           | 
           | For the "how many photons are needed" question, I agree that
           | 320 baud (i.e., the effective analog bandwidth of 320 Hz)
           | should have been used for the Shannon-Hartley calculations.
        
       | lordnacho wrote:
       | I love these kinds of questions. So what does that conclusion
       | mean about when the probe will be so far away that we are below
       | the Shannon limit?
       | 
       | And can we beat the Shannon limit somehow, eg collect for longer,
       | put the dish outside the atmosphere, and so on?
        
         | fsmv wrote:
         | Seems like we can just build a bigger receiving dish
        
           | rcxdude wrote:
           | There's not a lot of appetite for that, though. the 70m
           | receiver is already one of the largest ever built, and for
           | most use cases it's looking better to use an array of smaller
           | ones. Which works fine for receiving but not so much for
           | transmitting (while there are multiple sites in the world
           | capable of receiving from voyager 2, there's only one dish
           | which can actually transmit to it)
           | 
           | (I recall seeing a video on that dish, and the director
           | seemed confident there was enough noise margin left that
           | voyager's power would fail before they lost contact with it)
        
         | Asraelite wrote:
         | I guess we could just program Voyager 1 to lower the data
         | bitrate, adding more redundancy / error correction. I think
         | there's no real limit to how far it could get if we keep doing
         | that.
        
         | ethbr1 wrote:
         | Not my field, but assuming transmitting hardware (including
         | beam forming) is constant and that atmosphere can mostly be
         | ignored (see comments about it usually being a non-impact in
         | the transmission frequencies), two approaches would suggest:
         | 
         | 1. Increase the effective receiving dish size, to capture more
         | of the signal. Essentially, this would be effective in direct
         | proportion to beam spread (the more beam spread, the bigger
         | dish you can use to capture signal).
         | 
         | In practice, this would use multiple geographically-displaced
         | dishes to construct a virtually-larger dish, to allow for
         | better noise-cancellation magic (and at lower cost than one
         | huge dish). I believe the deep space network (DSN) already does
         | this? _Edit_ : It certainly has arrayed antennae [0], though
         | not sure how many are Voyager-tasked.
         | 
         | 2. Increase the resilience of the signal, via encoding. The
         | math is talking about bits and photons, but not encoded
         | information. By trading lower bit-efficiency for increased
         | error tolerance (i.e. including redundant information) we can
         | extract a coherent signal even accounting for losses.
         | 
         | Someone please point out if I'm wrong, but afaik the Shannon-
         | Hartley limit speaks to "lower" in the physical stack than
         | error coding. I.e. one can layer arbitrary error coding on top
         | of it to push limits (at the expense of rate)?
         | 
         | If the above understanding is correct, is there a way to
         | calculate maximum signal distance _assuming a theoretically
         | maximally efficient error coding_ (is that a thing?) ? Or is
         | that distance effectively infinite, assuming you 're willing to
         | accept an increasingly slow bit receiving rate?
         | 
         | [0]
         | https://en.m.wikipedia.org/wiki/NASA_Deep_Space_Network#Ante...
        
           | retrac wrote:
           | There's another major factor. I suppose it falls under the
           | encoding. Frequency stability. In a certain sense, having an
           | extremely precise oscillator at both the receiver and the
           | transmitter, is the same thing as just having a better more
           | frequency-stable antenna, or less noise in the channel
           | (because you know what the signal you're listening for should
           | look like).
           | 
           | I'm no physicist here so take this with a major grain of
           | salt. I think the limit might ultimately arise from the
           | uncertainty principle? Eventually the signal becomes so weak
           | that measuring it, overwhelms the signal. This is why the
           | receiver of space telescopes is cooled down with liquid
           | helium. The thermally-generated background RF noise (black
           | bodies radiate right down into the radio spectrum) would
           | drown everything else out otherwise.
           | 
           | Along those lines, while I'm still not quite sure where the
           | limit is, things become discrete at the micro level, and the
           | smallest possible physical state change appears to be
           | discrete in nature:
           | https://en.wikipedia.org/wiki/Landauer%27s_principle Enough
           | work physically must occur to induce a state change of some
           | kind at the receiver, or no communication can occur. (But
           | this interpretation is disputed!)
        
             | lxgr wrote:
             | Coding counters the uncertainty principle by allowing
             | multiple measurements, which can then be averaged. Thant
             | counters the contribution of random noise.
             | 
             | There are practical signals we use every day that are
             | "below the noise floor" before we decode them.
             | 
             | So while there is an ultimate limit of the maximum coding
             | rate for a given signal-to-noise ratio, this is expressed
             | in terms of a data rate (i.e. bits per second). If you're
             | fine with lowering your data rate, there is no fundamental
             | theoretical limit, as far as I understand.
        
           | shagie wrote:
           | The resilience of the signal part...
           | 
           | https://www.allaboutcircuits.com/news/voyager-mission-
           | annive...
           | 
           | > The uplink carrier frequency of Voyager 1 is 2114.676697
           | MHz and 2113.312500 MHz for Voyager 2. The uplink carrier can
           | be modulated with command and/or ranging data. Commands are
           | 16-bps, Manchester-encoded, biphase-modulated onto a 512 HZ
           | square wave subcarrier.
           | 
           | The "Manchester encoding" brings us to
           | https://www.allaboutcircuits.com/technical-
           | articles/manchest...
           | 
           | https://en.wikipedia.org/wiki/Manchester_code
           | 
           | Note that "16 bps" while the system runs at 160 bps. This
           | suggests that the data is repeated ten times and xor'ed with
           | a clock running at 10 HZ.
           | 
           | While there's no VOY set up now,
           | https://eyes.nasa.gov/dsn/dsn.html will occasionally show it.
           | When that happens, you will likely see two set up for it.
           | I've not seen them set up across multiple facilities - the
           | facilities are 120deg apart and only one has a spacecraft
           | above the horizon for any given length of time.
           | 
           | ---
           | 
           | In the "sensitivity to photons" category, I'll also mention h
           | ttps://en.wikipedia.org/wiki/Lunar_Laser_Ranging_experiment..
           | .
           | 
           | At the Moon's surface, the beam is about 6.5 kilometers (4.0
           | mi) wide[24][i] and scientists liken the task of aiming the
           | beam to using a rifle to hit a moving dime 3 kilometers (1.9
           | mi) away. The reflected light is too weak to see with the
           | human eye. Out of a pulse of 3x10^17 photons aimed at the
           | reflector, only about 1-5 are received back on Earth, even
           | under good conditions. They can be identified as originating
           | from the laser because the laser is highly monochromatic.
           | 
           | While there's no signal there, we're still looking at very
           | sensitive equipment.
        
           | RetroTechie wrote:
           | 3. Use relays.
           | 
           | Of course that would mean sending (a) giant receiver dish(es)
           | in the general direction a probe is sent. On the flip side,
           | if using a single relay it could travel at roughly 1/2 the
           | speed of the probe.
           | 
           | Note that signal strength weakens with distance^2. So if eg.
           | you'd have 2 relays (1/3 and 2/3 between Earth & the probe),
           | each relay would receive 9x stronger signal.
           | 
           | No doubt the 'logistics' (trajectory, gravity assist options,
           | mission cost etc) make this impractical. But it _is_ an
           | option.
        
             | ethbr1 wrote:
             | That'd be really cool! And definitely helped by the fact
             | that you'd only need to head out at a fraction of Voyagers
             | speeds to get the benefit.
             | 
             | There's some details on the Voyager gravity-assist
             | mechanics here [0], but you'd also need the escape
             | trajectory to be pointed in the Voyager direction which
             | would further constrain...
             | 
             | That said, Earth-Jupiter-Saturn alignments don't seem that
             | rare (on a decades scale).
             | 
             | [0] http://www.gravityassist.com/IAF3-2/Ref.%203-143.pdf
        
           | nsguy wrote:
           | TIL from another comment that the Shannon limit assumes
           | Gaussian noise so it's not actually always the theoretical
           | limit.
           | 
           | You can't work around the Shannon limit by using encoding.
           | It's the theoretical information content limit. But you can
           | keep reducing the bandwidth and one way of doing that is
           | adding error correction. So intuitively I'd say yes to your
           | question, the distance can go to infinity as long as you're
           | willing to accept an increasingly low receive bit rate.
           | What's less clear to me is whether error correction on its
           | own can be used to approach the Shannon limit for a given S/N
           | ratio - I think the answer is no because you're not able to
           | use the entire underlying bandwidth. But you can still
           | extract a digital signal from noise given enough of a
           | signal...
           | 
           | EDIT: There is a generalization of the Shannon limit to non-
           | white Gaussian noise here:
           | https://dsp.stackexchange.com/a/82840
        
         | mlok wrote:
         | Maybe some kind of relay in space (maybe it could follow
         | Voyager 1, slightly faster) which amplifies the signal and
         | retransmits to Earth ?
        
         | mpreda wrote:
         | Maybe multiple receiving antennas could be used, spaced widely
         | apart (e.g. one on Earth, one on the moon, one in orbit
         | somewhere); each would receive some signal affected by noise,
         | but the noise would be different for each (such as the
         | atmosphere affecting only the on-ground antenna). Also given
         | that we know the precise location of the transmitter, we can
         | work-out the exact phase difference between the antennas. Some
         | digital post-processing would combine the raw signal+noise from
         | the multiple receivers and extract the signal.
         | 
         | In fact, I assume that at this distance, even a very narrow
         | signal would spread wide enough to illuminate more than just
         | the Earth diameter.
        
         | Symmetry wrote:
         | The Shannon Limit is fundamental so you can't get around it
         | directly. But yes, there are things you can do to receive
         | information from further away.
         | 
         | 1) A bigger dish is the most obvious one.
         | 
         | 2) Use a lower bitrate to send more energy per bit at the same
         | transmitter power.
         | 
         | 3) Reduce the effective receiver temperature. This is a case
         | where putting it outside the atmosphere might help in reducing
         | noise.
        
         | 7373737373 wrote:
         | If the current number of photons per bit is 1500 and the
         | effective limit at 8.3GHz is 25, that is a factor of 60.
         | 
         | With each doubling of distance the number decreases by the
         | inverse square law, so with the current setup we'd have a
         | maximum distance of log2(60) = 5.9 times the current distance
         | (about 163 astronomical units (AU)) which is 961 AU.
         | 
         | In comparison, the closest star to our sun, Proxima Centauri,
         | is 268774 AU away!
         | 
         | Which means we would need something 268774/961 ~= 280 times
         | SQUARED = 78222 times more sensitive than the current setup at
         | the Shannon limit to communicate with it if it managed to get
         | that far.
        
         | kibwen wrote:
         | _> So what does that conclusion mean about when the probe will
         | be so far away that we are below the Shannon limit?_
         | 
         | I think the practical limit right now is that the Voyagers are
         | losing power.
         | 
         |  _" The radioisotope thermoelectric generator on each
         | spacecraft puts out 4 watts less each year. [...] The two
         | Voyager spacecraft could remain in the range of the Deep Space
         | Network through about 2036, depending on how much power the
         | spacecraft still have to transmit a signal back to Earth."_
         | 
         | https://voyager.jpl.nasa.gov/frequently-asked-questions/
        
         | Dylan16807 wrote:
         | > And can we beat the Shannon limit somehow, eg collect for
         | longer
         | 
         | If you turn on a faucet for longer, you're not beating the
         | "gallon limit" of the system. The limit is not a fixed number,
         | it's directly based on how much you do to improve the signal.
         | 
         | And they have already slowed down the transmission speed
         | repeatedly.
        
       | amirhirsch wrote:
       | TLDR; 4e22 photons per second 2.6e22 per bit.
       | 
       | For comparison, ~2e26 photons will be received through your iris
       | in your life
        
         | KeplerBoy wrote:
         | Does this number account for all photons or just those in the
         | rather narrow optical band?
         | 
         | Then again RF photons just don't fit through the pupils and
         | will get backscattered, i guess.
        
         | amelius wrote:
         | How many of them come from Voyager 1?
        
           | amirhirsch wrote:
           | Someone's asking the hard questions! According to the oracle,
           | 1 in 4 people will experience one photon from voyager in
           | their lifetime.
        
         | rcxdude wrote:
         | That's how many are _sent_ by Voyager. Only about 1500 or 400
         | photons per bit are actually received by the radio dish
         | (depending on which frequency is being used).
        
           | croemer wrote:
           | Maybe OP sends photons from their eyes in addition to
           | receiving them
        
       | pcdoodle wrote:
       | I am confused. I thought photons were just visible light but I
       | guess these little buggers are everywhere. Also very surprised
       | voyager is using 2.3ghz, that's crazy saturated on earth due to
       | wifi. How these engineers make this all work, is magic to me.
        
         | mpreda wrote:
         | _Electromagnetic radiation_ includes visible light, radio
         | spectrum, X-rays, etc. Photons.
        
         | nilamo wrote:
         | > Also very surprised voyager is using 2.3ghz, that's crazy
         | saturated on earth due to wifi
         | 
         | Wifi didn't exist when Voyager was launched...
        
           | thsksbd wrote:
           | But the band was free for use, wasn't it? (Obviously not
           | crowded)
        
             | anotherhue wrote:
             | Available for microwaves since 1947, intentional emission
             | came later in the 80s.
        
             | ianburrell wrote:
             | The ISM band is 2.4-2.5 GHz. Voyager at 2.3Ghz is outside
             | the band.
        
         | drmpeg wrote:
         | WiFi is at 2.4 GHz. LTE band 30, satellite radio (XM/Sirius)
         | and aeronautical telemetry all exist between the deep space
         | downlink at 2290 to 2300 MHz and WiFi at 2400 MHz.
        
         | noneeeed wrote:
         | Nope. It's one of those things that can take a bit to get used
         | to, but everything on the electromagnetic spectrum is just
         | light in the general sense. The only difference between radio-
         | waves, x-rays, infra-red and (human) visible light is the
         | frequency/wavelength.
         | 
         | If the frequency is high enough then the waves of light can be
         | detected by things as small as cells in the back of your eye,
         | or the pixels in a camera sensor. If it is too low then you
         | need much larger detectors.
         | 
         | Other animals have detectors for different
         | frequencies/wavelengths, allowing them to see either infra-red
         | (mosquitos) or ultraviolet (bees, butterflies etc).
         | 
         | What we call "visible light" is just the particular range that
         | our eyes can detect (about 400 to 800THz). If we were the size
         | of a planet, and our eye cells were the size of a radio-
         | telescope dish we would be able to "see" in those wavelengths.
         | In fact, when we see images taken by radio telescopes, those
         | have been essentially pitch-shifted up to something we can see,
         | like the reverse of what we do when listening for bat clicks
         | (where the pitch is downshifted to our hearing range).
         | 
         | The wikipedia article has a nice little diagram putting the
         | wavelengths into perspective.
         | https://en.wikipedia.org/wiki/Electromagnetic_spectrum
        
           | pcdoodle wrote:
           | Thanks for the reply.
           | 
           | This makes me think of the dual slit experiment. Does the
           | universe treat everything as a wave to save CPU cycles or
           | something?
           | 
           | If we think of light as little balls (at our size i think
           | that would make sense). If we were much bigger, we would
           | think of these longer waves as balls too?
        
             | SJC_Hacker wrote:
             | Wave-particle duality/quantum mechanics have different
             | interpretations, but since "the math works" and there's
             | nothing better, thats what they go with.
             | 
             | One way of thinking of it - everything is a wave until you
             | make a measurement. Then you get a "collapse"
             | (localization) of the wavefunction. Which leads to the
             | question of why the wave function collapses - i.e. how does
             | nature know we want to make a measurement.
             | 
             | Which leads to all sorts of crazy ideas like the simulation
             | hypothesis. Which is not a scientific theory, because you
             | can't falsify it, but even very educated people like Neil
             | DeGrasse Tyson have remarked on it.
        
         | pythonguython wrote:
         | Photons and waves both model electromagnetism. Photons are just
         | the quantization of electromagnetic radiation, where E=hv. This
         | is the whole idea of wave-particle duality. We often describe
         | radio frequencies with waves because they act more like waves
         | than particles (Diffraction, spherical propagation, have an
         | easily measureable wavelength)
        
         | einsteinx2 wrote:
         | Photons are just the quanta or particles of electromagnetic
         | radiation, of which visible light is a small portion of the
         | overall spectrum. So you can have photons of microwaves as
         | well, such as in this case. Or photons of X-rays or gamma rays
         | or infrared light or ultraviolet light or whatever. It's pretty
         | wild actually just how small a section of the EM spectrum our
         | eyes are sensitive to!
        
         | BenjiWiebe wrote:
         | 2.3 GHz is not saturated due to WiFi. Wifi is 2.4GHz and up.
         | Even the harmonics will be above 2.4 GHz (by definition).
        
       | moffkalast wrote:
       | You know, I never really thought of lower wavelengths than light
       | as being carried by photons, but I suppose it's all EM. Antennas
       | are technically just really red light bulbs.
        
         | gjstein wrote:
         | This is true enough, though remember that material properties
         | change dramatically when you start moving through wavelengths
         | by orders of magnitude. Silicon is transparent in the mid-
         | infrared, which is what makes silicon photonics possible [1]
         | 
         | [1] https://en.wikipedia.org/wiki/Silicon_photonics
        
       | bandrami wrote:
       | It's crazy to me how many theoretical limits Shannon predicted
       | way before the hardware was there.
        
         | ziofill wrote:
         | That's because his results are about pure information (and in
         | the limit for infinite string lengths), so sooner or later some
         | hardware will hit onto those limits or tend to them.
        
           | bandrami wrote:
           | Agreed, but: he's still understudied. I think in retrospect
           | any 21st-century math course has to include Shannon, and they
           | don't all, yet.
        
             | sebzim4500 wrote:
             | On some level he's a victim of his own success. He invents
             | information theory in the same paper that proves the most
             | interesting results, so who else will work on it?
        
               | aidenn0 wrote:
               | Even the practical work was done surprisingly early. I
               | have a book on error correcting codes from the 1950s and
               | it's missing very little (Most notably trellis codes and
               | LDPC; the former being invented in the '70s and the
               | latter in 1963).
        
               | sebzim4500 wrote:
               | There's been much more progress on compression though
               | (Arithmetic Coding, ANS, etc.)
        
               | moffkalast wrote:
               | Shannon: "I'm about to make and end this field's whole
               | career."
        
       | Strilanc wrote:
       | Wasn't expecting my question to hit top of HN. I guess I'll give
       | some context for why I asked it.
       | 
       | I work in quantum error correction, and was trying to collect
       | interesting and quantitative examples of repetition codes being
       | used implicitly in classical systems. Stuff like DRAM storing a 0
       | or 1 via the presence or absence of 40K electrons [1], undersea
       | cables sending X photons per bit (don't know that one yet), some
       | kind of number for a transistor switching (haven't even decided
       | on the number for that one yet), etc.
       | 
       | A key reason quantum computing is so hard is that by default
       | repetition makes things worse instead of better, because every
       | repetition is another chance for an unintended measurement. So
       | protecting a qubit tends to require special physical properties,
       | like the energy gap of a superconductor, or complex error
       | correction strategies like surface codes. A surface code can
       | easily use 1000 physical qubits to store 1 logical qubit [2], and
       | I wanted to contrast that with the sizes of implicit repetition
       | codes used in classical computing.
       | 
       | 1: https://web.mit.edu/rec/www/dramfaq/DRAMFAQ.html
       | 
       | 2: https://arxiv.org/abs/1208.0928
        
         | nico wrote:
         | Very cool. It's interesting to realize that at some level,
         | every system is a quantum system if you "zoom in" enough
        
           | Ringz wrote:
           | I would spontaneously respond that you are right and at the
           | same time have no problem if someone explains to me that it
           | is not so.
        
           | empyrrhicist wrote:
           | I think the point is the model though - if a system's
           | behavior can be modeled/described classically, it's a bit
           | silly to to call it a "quantum" system in the same way that
           | it's reductive to say Biology is just applied particle
           | physics. Sure, but that's not a very useful level of
           | abstraction.
        
             | jessriedel wrote:
             | If you want to understand the transition between a
             | fundamental theory and its effective description in some
             | limiting regime, you need to be able to describe a system
             | in the limiting regime using the fundamental theory. It's
             | not "silly" to talk about an atom having a gravitational
             | field even if it's unmeasurably small (currently).
        
           | fsckboy wrote:
           | > _at some level, every system is a quantum system_
           | 
           | if we consider "quantum" to mean our quantum theory, at the
           | level of general relativity, gravity is not a quantum system.
           | and the qualifier "yet" is also not known.
        
         | grog454 wrote:
         | > by default repetition makes things worse instead of better
         | 
         | Can you elaborate on this a bit? My intuition is that, by
         | default, statistical models benefit from larger N. But I have
         | no experience in quantum physics.
        
           | ziofill wrote:
           | It actually depends how this sentence is intended. There
           | exist quantum repetition codes: the Shor code is the simplest
           | example that uses 9 physical qubits per logical qubit. Since
           | the information is quantum it needs majority voting over two
           | independent bases (hence 3x3=9 qubits to encode a logical
           | one).
        
           | Strilanc wrote:
           | It's because unintended measurement is a type of error in a
           | quantum computer. Like, if an electron passing near your
           | qubit would get pushed left if your qubit was 0 and right if
           | was 1, then you will see errors when electrons pass by.
           | Repeating the 0 or 1 a thousand times just means there's
           | 1000x more places that electrons passing by would cause a
           | problem. That kind of redundancy makes that kind of error
           | mechanism worse instead of better.
           | 
           | There _are_ ways of repeating quantum information that
           | protect against accidental measurement errors. For example,
           | if your logical 0 is |000 > + |110> + |011> + |101> and your
           | logical 1 is |111> + |001> + |100> + |010> then can recover
           | from one accidental measurement. And there are more complex
           | states that protect against both bitflip errors and
           | accidental measurements simultaneously. They're just more
           | complicated to describe (and implement!) than "use 0000000
           | instead of 0 and 1111111 instead of 1".
        
             | Kerbonut wrote:
             | If there's interference, could you do something like when
             | using 7 repetition for each bit, take whatever 5 of 7 is,
             | e.g. 1111100 is 1 and 1100000 is 0.
        
             | nomel wrote:
             | Is this the correct interpretation?
             | 
             | Classical systems: You measure some state, with the
             | measurement containing some error. Averaging the
             | _measurement error_ usually gets closer to the actual
             | value.
             | 
             | Quantum systems: Your measurement influences/can influence
             | the state, which can cause an error in the state itself.
             | Multiple measurements means more possible influence.
        
               | Strilanc wrote:
               | Yeah that's roughly it. In classical computers all errors
               | can be simplified as being bit flip errors (0 instead of
               | 1, 1 instead of 0). Like, power loss is a lot of bit flip
               | errors that happened to target the bits that should have
               | been 1. In quantum computers this simplification does not
               | work, there is another type of error called a phase flip.
               | Measurements cause phase flip errors. You can exchange
               | the phase flip and bit flip bases by using a gate called
               | the Hadamard gate. So if you surround measurements with
               | Hadamard gates, you will see bit flip errors. The
               | existence of gates like Hadamard is what makes it
               | possible to see these kinds of things at all, and
               | correspondingly its availability can be thought of as the
               | thing that makes a quantum computer a quantum computer,
               | instead of a classical computer.
        
           | Sniffnoy wrote:
           | You might be making the mistake of thinking that quantum
           | mechanics runs on probabilities, which work in the way you
           | are used to, when in fact it runs on amplitudes, which work
           | quite differently.
        
         | cycomanic wrote:
         | Subsea cables don't use repetition codes (they are very much
         | suboptimal), but typically use large overhead (20%) LDPC codes
         | (as do satellite comms systems for that matter (the dvb-s2
         | standard is a good example). Generally to get anywhere close to
         | Shannon we always need sophisticated coding.
         | 
         | Regarding the sensitivity of Subsea systems they are still
         | significantly above 1 photon/bit, the highest sensitivity
         | experiments have been done for optical space comms (look e.g.
         | for the work from Mit Lincoln Labs, David Geisler, David Kaplan
         | and Bryan Robinson are some of the people to look for.
        
           | Strilanc wrote:
           | I think you're picturing a different level of the network
           | stack than I had in mind. Yes, above the physical level they
           | will be explicitly using very sophisticated codes. But I
           | think physically it is the case that messages are transmitted
           | using pulses of photons, where a pulse will contain many
           | photons and will lose ~5% of its photons per kilometer when
           | travelling through fiber (which is why amplifiers are needed
           | along the way). In this case the "repetition code" is the
           | number of photons in a pulse.
        
             | cycomanic wrote:
             | But we are classical, so I think it's wrong (or at least
             | confusing) to talk about the many photons as repetition
             | codes. Then we might as well start to call all classical
             | phenomena repetition codes. Also how would you define SNR
             | when doing this?
             | 
             | Repetition codes have a very clearly defined meaning in
             | communication theory, using them to mean something else is
             | very confusing.
        
               | jessriedel wrote:
               | > Then we might as well start to call all classical
               | phenomena repetition codes
               | 
               | All classical phenomena _are_ repetition codes (e.g.,
               | https://arxiv.org/abs/0903.5082 ). And this is perfectly
               | compatible with the meaning in communication theory,
               | except that the symbols we're talking about are the
               | states of the fundamental physical degrees of freedom.
               | 
               | In the exact same sense, the von Neumann entropy of a
               | density matrix is the Shannon entropy of its spectrum,
               | and no one says "we shouldn't call that the Shannon
               | entropy because Shannon originally intended to apply it
               | to macroscopic signals on a communication line".
        
               | Strilanc wrote:
               | Yeah, I agree it's unusual to describe "increased
               | brightness" as "bigger distance repetition code". But I
               | think it'll be a useful analogy in context, and I'd of
               | course explain that.
        
         | fsckboy wrote:
         | > _How many photons are received per bit transmitted from
         | Voyager 1?_
         | 
         | wouldn't you also want to know how many photons are transmitted
         | and how many bits transmitted are received?
        
           | stracer wrote:
           | All transmitted bits are also received, at least when
           | everything works as intended.
        
             | forgot-im-old wrote:
             | No, with error correction, not all transmitted bits are
             | received, but the message bits can be recovered.., and if
             | not they must retransmit later.
        
         | resters wrote:
         | Isn't sending more than one photon always "repetition" in that
         | sense? Classical systems probably don't do that because of the
         | engineering complexity of sending a single photon at a time --
         | we had oscillators and switches, not single photon emitters.
        
           | jessriedel wrote:
           | > Isn't sending more than one photon always "repetition" in
           | that sense?
           | 
           | Yes. But regardless of whether its feasible to send single
           | quanta in any given circumstance, the redundant nature of the
           | signals is key to understanding its much higher degree of
           | robustness relative to quantum signals.
           | 
           | And to be clear, you can absolutely send a classical signal
           | with individual quanta.
        
         | s1dev wrote:
         | I believe that a classical radio receiver is measuring a
         | coherent state. This is a much lower level notion than people
         | normally think about in QEC since the physical DoF are usually
         | already fixed (and assumed to be a qubit!) in QEC. The closest
         | analogue might be different choices of qubit encodings in a
         | bosonic code.
         | 
         | In general, I'm not sure that the classical information theory
         | toolkit allows us to compare a coherent state with some average
         | occupation number N to say, M (not necessarily coherent) states
         | with average occupation number N' such that N' * M = N. For
         | example, you could use a state that is definitely not
         | "classical" / a coherent state or you could use photon number
         | resolving measurements.
         | 
         | A tangential remark: The classical information theory field
         | uses this notion of "energy per bit" to be able to compare more
         | universally between information transmission schemes. So they
         | would ask something like "How many bits can I transmit with X
         | bandwidth and Y transmission power?"
        
         | Sharlin wrote:
         | > Stuff like DRAM storing a 0 or 1 via the presence or absence
         | of 40K electrons
         | 
         | I'd assume that these days it's a couple of orders of magnitude
         | fewer than that (the cited source is from 1996). Incidentally,
         | 40k e- is roughly the capacity of a single electron well
         | ("pixel") in a modern CMOS image sensor [1] - but those 40k
         | electrons are able to represent a signal of up to ~14 bits,
         | around 10k distinct luminance values, depending on temperature
         | and other noise sources.
         | 
         | [1] https://www.princetoninstruments.com/learn/camera-
         | fundamenta...
        
           | Strilanc wrote:
           | If you have a more modern estimate I'll take it. Very
           | interesting about the CMOS sensors distinguishing +- 2
           | electrons (40K / 2^14).
        
         | dheera wrote:
         | I worked in quantum optics for a while. Our DARPA grant once
         | had the "mission" to see how many bits of information could be
         | theoretically crammed into 1 photon. It turns out to be an
         | uninteresting question because you can theoretically cram
         | infinite bits into one photon, encoded in the relative timing
         | of the photon in a pulse train, limited only by the dispersion
         | of your medium (in space, effectively zero).
         | 
         | Even dispersion is a boring question because it is possible to
         | reverse dispersion by sending the light through a parametric
         | amplifier to conjugate the phases and then running it through
         | the dispersion medium a second time locally.
         | 
         | We later ended up working on other things.
        
       | cycomanic wrote:
       | Actually the limit predicted by Shannon can be significantly
       | beaten, because Shannon assumes gaussian noise, but if we use
       | photon counting receivers we need to use a poisson distribution.
       | This is the Gordon-Holevo limit.
       | 
       | To beat Shannon you need PPM formats and photon counters (single
       | photon detectors).
       | 
       | One can do significantly better than the numbers from voyager in
       | the article using optics even without photon cpunting. Our group
       | has shown 1 photon/bit at 10 Gbit/s [1] but others have shown
       | even higher sensitivity (albeit at much lower data rates).
       | 
       | [1] https://www.nature.com/articles/s41377-020-00389-2
        
         | nico wrote:
         | Interesting. Is that related to compressed sensing? I wonder if
         | compress sensing could be used for something like the Voyager
         | signals
         | 
         | It seems there might be multiple ways to go beyond Shannon's
         | limit, depending on what you are trying to do
        
           | cycomanic wrote:
           | I don't think compressed sensing is really extracting more
           | information than Shannon, it simply exploits the fact that
           | the signal we are interested in is sparse so we don't need to
           | sample "everything". But this is somewhat outside my area of
           | expertise so my understanding could be wrong.
        
             | nico wrote:
             | Maybe I'm mixing Shannon's limit with the sampling rate
             | imposed by the Nyquist-Shannon Sampling theorem
             | 
             | > Around 2004, Emmanuel Candes, Justin Romberg, Terence
             | Tao, and David Donoho proved that given knowledge about a
             | signal's sparsity, the signal may be reconstructed with
             | even fewer samples than the sampling theorem
             | requires.[4][5] This idea is the basis of compressed
             | sensing
             | 
             | ...
             | 
             | > However, if further restrictions are imposed on the
             | signal, then the Nyquist criterion may no longer be a
             | necessary condition. A non-trivial example of exploiting
             | extra assumptions about the signal is given by the recent
             | field of compressed sensing, which allows for full
             | reconstruction with a sub-Nyquist sampling rate.
             | Specifically, this applies to signals that are sparse (or
             | compressible) in some domain
             | 
             | From: https://en.m.wikipedia.org/wiki/Nyquist%E2%80%93Shann
             | on_samp...
        
               | sunk1st wrote:
               | In so many words, Shannon gave a proof showing that _in
               | general_ the sample rate of a digital sensor puts an
               | upper bound on the frequency of any signal that sensor is
               | able to detect.
               | 
               | Unlike the Nyquist-Shannon theory, compressed sensing is
               | not generally applicable: it requires a sparse signal.
               | 
               | As with many other optimization techniques, it's a trade
               | off between soundness and completeness.
        
               | nico wrote:
               | Great way to explain it!
               | 
               | Loved this:
               | 
               | > As with many other optimization techniques, it's a
               | trade off between soundness and completeness
        
         | ramraj07 wrote:
         | Can't you calculate the CRLB for any given distribution if you
         | wanted? That's what my lab did for microscopy anyway. Saying
         | you're beating the Shannon limit is like saying you're beating
         | the second law of thermodynamics to me.. but I could be wrong.
        
           | Sanzig wrote:
           | You are correct. People often say "Shannon limit" (the
           | general case) when they are really referring to the "Shannon-
           | Hartley Limit" (the simplified case of an additive white
           | Gaussian noise channel).
           | 
           | For example, MIMO appears to "break" the Shannon-Hartley
           | limit because it does exceed the theoretical AWGN capacity
           | for a simple channel. However, when you apply Shannon's
           | theory to reformulate the problem for the case of a multipath
           | channel with defined mutual coupling, you find that there is
           | a higher limit you are still bounded by.
        
             | s1dev wrote:
             | I often wondered why MIMO was such an investigated topic.
             | It would make sense if the Shannon limit is higher for this
             | channel. Is there a foundational paper or review that shows
             | this?
        
           | cycomanic wrote:
           | Shannon theory assumes Gaussian noise, however in the very
           | low power regime that's just not true. I agree it's
           | unintuitive. Have a look at the Gordon paper I posted
           | earlier.
        
         | aptitude_moo wrote:
         | Very interesting, I studied telecommunications and I thought
         | the Shannon limit was the absolute limit. I wonder now if this
         | Gordon Holevo limit is applicable for "traditional"
         | telecommunications (like 5G) as opposed to photon counting a
         | deep space probe
         | 
         | EDIT: This paper seems to answer my question [1]
         | 
         | [1]
         | https://opg.optica.org/directpdfaccess/8711ab35-bbc2-4d51-8e...
        
           | stracer wrote:
           | Can you please post another link? This one does not work.
        
             | HappyPanacea wrote:
             | I think it is https://arxiv.org/abs/2002.05766.
        
             | richarme wrote:
             | I think it's this one:
             | 
             | https://opg.optica.org/jlt/viewmedia.cfm?uri=jlt-38-10-2741
             | &...
             | 
             | Quantum Limits in Optical Communications
             | 
             | Konrad Banaszek, Ludwig Kunz, Michal Jachura, and Marcin
             | Jarzyna
        
           | adrian_b wrote:
           | As also explained in the conclusion of the paper linked by
           | you, "photon-counting" detectors are possible only when the
           | energy of one photon is high enough, which happens only for
           | infrared light or for higher frequencies.
           | 
           | "Photon-counting" methods cannot be implemented at
           | frequencies so low as used in 5G networks or in any other
           | traditional radio communications.
        
             | IndrekR wrote:
             | /at room temperature/
             | 
             | https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise
        
         | stracer wrote:
         | Is there some fundamental limit to the number of bits per
         | photon that can be communicated via EM radiation? I think it
         | does not exist, because photons aren't all equal, we can use
         | very high frequency and X-ray quantum can probably carry much
         | more information than RF quantum.
        
           | resters wrote:
           | this is called the Shannon limit. To discern signal from
           | noise, a minimum sample rate of 2x the frequency of the
           | signal is required. A signal is something that can be turned
           | on or off to send a bit.
           | 
           | Higher frequencies can carry more data as you infer but the
           | engineering challenges of designing transmitters and
           | receivers create tradeoffs in practical systems.
        
             | ganzuul wrote:
             | In addition to wavelength EM also has several polarization
             | modes and near/far field characteristics that can carry
             | information.
        
               | resters wrote:
               | Can individual photons be measured for polarization and
               | phase or is there a similar limit that requires more than
               | one photon to do so? I suppose both are relative to some
               | previous polarization or phase?
        
           | ganzuul wrote:
           | Good induction to thinking about quantum gravity.
        
           | im3w1l wrote:
           | Send three photons A B C. They arrive at times ta, tb, tc.
           | Compute fraction (tc - tb) / (tb - ta). This can encode any
           | positive real number with arbitrary precision. But clearly
           | you need either very precise measurements or send the photons
           | at a very slow rate.
        
           | yyyfb wrote:
           | I guess not without a minimum bound on the communication
           | speed.
           | 
           | If you have a way to reliably transmit N bits in time T using
           | P photons, you can transmit N+1 bits in time 2 * T using also
           | P photons. What you would do to transmit X0,X1,...Xn is:
           | 
           | - During the first time slot of duration T, transmit X1,...
           | Xn if X0 = 0 and 0 otherwise (assuming absence of photons is
           | one of the symbols, which we can label 0)
           | 
           | - During the second time slot of duration T, transmit 0 if
           | X0=0 and X1,... Xn otherwise
           | 
           | This only uses P photons to transmit one more bit, but it
           | takes twice as long. So if you're allowed to take all the
           | time that you want to transmit, and have really good clocks,
           | I guess that theoretically this is unbounded.
        
         | sansseriff wrote:
         | The Deep Space Optical Communication (Dsoc) between earth and
         | the psyche spacecraft uses large-M PPM for this reason! This
         | mission is currently ongoing.
         | 
         | They send optical pulses in one of up to 128 possible time
         | slots, thereby carrying 7 bits each. And each optical pulse on
         | earth may only be received by 5-10 photons.
        
       | ziofill wrote:
       | What a lovely question. The estimate is 10-100 photons/bit
       | (minimum).
       | 
       | If you're curious about how many bits a _single_ photon can
       | carry, in controlled settings (tabletop quantum optics) a single
       | photon can carry log(n) bits where n is the size of the state
       | space of the photon, which theoretically is infinite and in
       | practice it can reach into the hundreds /thousands.
        
         | layer8 wrote:
         | No, the estimate is around 750 or 200 photons/bit received,
         | depending on the transmission frequency. The answer to the
         | question is B, not C. Your numbers are the estimated minimum
         | needed, not the actual amount received, which is what the
         | question was asking.
        
         | mnw21cam wrote:
         | Visible light is different, because each photon has a lot more
         | energy than in the 2.3GHz range. Your average decent consumer-
         | level camera has a sensor that can nominally just about detect
         | single photons some proportion of the time (as in, some of them
         | bounce off instead of being detected) though it can't
         | technically _count_ them. The graininess on digital camera
         | images is more from the Poisson noise of the incoming photons
         | than it is from the applied noise of the sensor itself.
        
       | HarHarVeryFunny wrote:
       | The fact that we can communicate with Voyager, and in both
       | directions, blows my mind. It's completely counter-intuitive.
       | 
       | At least for Voyager->earth we can use giant radio telescopes to
       | detect the faint signal, but how do we manage to focus on those
       | few hundreds of photons per bit coming from a pinpoint source a
       | light day away?!
       | 
       | In the earth->Voyager direction it seems even less intuitive -
       | sure we can broadcast a powerful signal, but it's being received
       | by a 12' wide antenna 15 billion miles away. WTF?
       | 
       | I guess radio communications in general is magic, a bit like (in
       | nature of counter-intuition) quantum entanglement of particles
       | arbitrarily far apart. It seems there is something deeply wrong
       | about our mental models of space and time.
        
       | cycomanic wrote:
       | For anyone who is interested in the ultimate limits to
       | communications the seminal paper by Jim Gordon is quite easy to
       | understand even without a physics degree (unlike the Holevo paper
       | IMO). He was incredibly good at writing in an accessible manner
       | (apart from probably being the person who most deserved a Nobel
       | prize but didn't get it).
       | 
       | https://doi.org/10.1109%2FJRPROC.1962.288169
        
         | prof-dr-ir wrote:
         | > probably being the person who most deserved a Nobel prize but
         | didn't get it
         | 
         | You probably want to read up a bit on the remarkable life of
         | Lise Meitner.
        
       | superposeur wrote:
       | The overwhelming loss in this calculation is from the antenna's
       | radiated energy spreading out over a larger and larger area
       | (despite the directional "gain" factor).
       | 
       | I'm wondering: would a probe launched today instead employ a
       | laser to communicate? This would seem to offer many orders of
       | magnitude improvement in the directionality of the signal.
        
         | deelowe wrote:
         | I imagine it'd certainly employ some type of beamforming at the
         | least.
        
           | wongarsu wrote:
           | Assuming you don't need fast steering, is a 3.7m transmitter
           | array doing beamforming really better than a 3.7m dish
           | transmitting at the same power?
           | 
           | My intuition would have been that you are better off using a
           | fairly standard transceiver and spending your engineering
           | budget either increasing power or getting a bigger dish
           | (either by launching on a wider rocket or with a folding
           | design).
           | 
           | Lasers might interesting for the downlink, but receiving a
           | laser signal on the probe sounds difficult (earth is pretty
           | bright).
        
             | cycomanic wrote:
             | Diffraction scales inversely proportional to wavelength so
             | you gain significantly by going to optics, i.e. you can use
             | a much smaller aperature in optics.
        
             | outworlder wrote:
             | There's some value in getting rid of mechanical devices (or
             | reducing the need to rotate the entire spacecraft).
        
             | CamperBob2 wrote:
             | The array doing beamforming can be spread out much farther.
             | If the DSN were being built now, I'd think its antennas
             | would look more like the Square Kilometer Array.
        
               | magicalhippo wrote:
               | Seems they're already on to something like that[1][2]:
               | 
               |  _We envision deployment in three sites at or near the
               | longitudes of the existing DSN sites._
               | 
               |  _As an example, a potential initial phase could deploy
               | 40 12-m elements at each complex to duplicate the X-band
               | performance of a DSN 70-m antenna._
               | 
               |  _Second and third phase deployments may bring the number
               | of 12-m antennas to 200, then perhaps 400 per complex._
               | 
               | [1]: https://ieeexplore.ieee.org/document/4374100
               | 
               | [2]: https://ieeexplore.ieee.org/document/4374103
        
         | londons_explore wrote:
         | The main challenge is the earth to probe comms for distant
         | probes, since the earth is often very close (in an angular
         | sense) to the sun from the probes perspective, and the sun
         | gives out a lot of black body radiation.
         | 
         | However, due to the shape of the black body radiation curve,
         | the sun gives out relatively less microwave radiation than it
         | does visible light, which might outweigh the advantages of more
         | directionality given by using a laser.
        
           | jjk166 wrote:
           | Further, we're good at building really big radio transceivers
           | here on Earth, we don't have nearly the same technical
           | experience with lasers of that scale.
        
           | superposeur wrote:
           | Ok what about using a maser instead of a laser?
        
             | opwieurposiu wrote:
             | The big dish antennas do use ruby masers, but not to
             | transmit. The maser is used as the LNA on the receive side.
             | Check out the picture on page 41 of the pdf, clearly this a
             | flux capacitor, mislabeled to deceive us ;)
             | 
             | https://descanso.jpl.nasa.gov/monograph/series10/03_Reid_ch
             | a...
             | 
             | https://www.rfcafe.com/references/popular-
             | electronics/amazin...
        
               | superposeur wrote:
               | Cool use of maser for receive.
               | 
               | Not having thought this through before, I see now that
               | while a transmit maser may have efficiency advantages, it
               | may not improve directionality relative to a standard
               | parabolic radio transmitter. All methods of producing
               | microwaves will have basically the same diffraction-
               | limited gain for a given "aperture" (dish) size. That
               | darn uncertainty principle! (However, an optical laser
               | would still give way better directionality.)
        
           | sebzim4500 wrote:
           | Presumably though it would be useful to have a high bandwidth
           | link back to earth even if we had to use conventional
           | microwave transmitters to send data back.
           | 
           | We want to download high resolution images/spectrographs
           | whereas we only want to upload code/instructions.
        
         | Out_of_Characte wrote:
         | There's several projects for laser-based communication and
         | research. It would also make it really difficult to aim since
         | you can miss your target now.
         | 
         | https://www.jpl.nasa.gov/news/nasas-deep-space-optical-comm-...
         | 
         | https://en.m.wikipedia.org/wiki/Laser_Interferometer_Space_A...
        
           | superposeur wrote:
           | Interesting about the JPL program and I'm amazed this
           | prototype was only launched last year! Apparently the answer
           | to comms laser use is "not yet but soon".
        
         | cycomanic wrote:
         | All space agencies have optical comms in their road maps.
         | Largely they are thinking about inter satellite communications
         | (the atmosphere causes significant issues when going back to
         | earth). So the main application is to have some relay satellite
         | that can then transmit to earth via RF. The application is not
         | mainly deep space ropes but Leo or meo satellites, the
         | typically only have very short transit times over the ground
         | stations, so can't get all their measurement data down. By
         | using e.g. a geo relay they can transmit lots of data optically
         | and the geo relay can more slowly transmit the data to earth
         | until the leo satellite comes back in view.
        
         | mordae wrote:
         | Improving directionality also makes aiming much harder.
        
         | sunk1st wrote:
         | Perhaps we should consider relaying the signal through a third
         | satellite.
        
         | CobrastanJorji wrote:
         | I'm curious about the feasibility of combining the two problems
         | of propulsion alway from Earth and communication with Earth
         | into beam-powered propulsion aimed directly at Earth, pulsed
         | for use as communication.
         | 
         | Probably infeasible for several reasons (only useful when
         | accelerating DIRECTLY away from Earth, incoming light to power
         | spaceship is probably coming from the sun and therefore likely
         | also in the directly of Earth, so net zero acceleration at best
         | from firing the photons back towards the sun), but it'd be
         | pretty neat.
        
       | hammock wrote:
       | >Voyager sends 160 bits/second
       | 
       | This makes me wonder, are the bits = the power turned on for
       | exactly 1/320th sec, every 1/160th sec? Or is the power on/power
       | off ratio something different? Does it vary by protocol? What are
       | the pros and cons?
        
         | danbruc wrote:
         | Without looking up what kind of encoding and modulation they
         | are using, I would assume that they are sending a continuous
         | sine wave at the carrier frequency that has the bits - probably
         | after encoding the raw data bits with some error correction
         | code - modulated onto it by changing frequency, amplitude,
         | phase, or a combination of them depending on the value of each
         | bit or group of bits.
        
       | ks2048 wrote:
       | Nice question. Does anyone know what exactly data is being sent?
       | What kind of compression it is using? etc
        
       | mooktakim wrote:
       | Why didn't they send out new relays as Voyager travelled out.
        
       | somat wrote:
       | An interesting thing about photons (which may not be true, I just
       | enjoy this stuff amateurishly, that is, without the effort or
       | rigor to actually understand it.) is that they might not exist.
       | the em field is not quantized, or at least is not quantized at
       | the level of photons. A "photon" only exists where the em field
       | interacts with matter, where the electrons that create the
       | disturbance can only pulse in discrete levels.
       | 
       | https://www.youtube.com/watch?v=ExhSqq1jysg
       | 
       | Not that this changes anything, we can only detect or create
       | light with matter. but it does make me curious about single
       | photon experiments and what they are actually measuring.
        
         | leetrout wrote:
         | Thanks for the link. I never conceptualized photons outside of
         | the visual spectrum so the headline made me take a step back
         | and get nerd sniped in the process.
         | 
         | I stumbled upon this before seeing your comment:
         | 
         | https://physics.stackexchange.com/questions/90646/what-is-th...
        
         | golergka wrote:
         | Isn't that simply the principle of particle-wave duality? When
         | particle/wave in field X interacts with field X, it behaves
         | like a wave, but interactions with other fields are quantised.
        
       | croemer wrote:
       | That's why I love Physics and was enamoured with it in my late
       | teens.
        
       | wwarner wrote:
       | 23 watts.
        
       | tb0ne wrote:
       | Super interesting! But I feel like there is a bit of a conclusion
       | missing for me.
       | 
       | So 1500 Photons hit the receiver per bit send, but this is
       | obviously way to few to keep processing the signal and it will
       | just be drowned out by noise? Where do we go from here? Does
       | voyager repeat its signal gazillions of times so we can average
       | out the noise on our end? Where can I find more information on
       | what is done with these few photons?
        
         | SonOfLilit wrote:
         | No, those 1500 photons are enough and we basically read the
         | signal from them, from my reading of the comments here.
        
       | PeterCorless wrote:
       | I just wanted to chime in with a reminder that though Voyager 1
       | is speeding away from Sol at a constant velocity because of the
       | Earth's revolution around the sun it can be up to +-1 AU closer
       | or further away, depending on the time of the year.
       | 
       | This article is for Voyager 2, but the issue is the same. For a
       | brief moment every year we actually get _closer_ to Voyager 1,
       | then we pivot away in our revolution around the sun and the
       | distance between Earth and Voyager 1 or 2 increases sharply. So
       | distance, when plotted over time, looks like a wobbly line.
       | 
       | https://earthsky.org/space/voyager-spacecraft-getting-closer...
        
       | rocho wrote:
       | Wow, I never thought about how Voyager communicates with Earth.
       | But now I wonder: if Voyager just sends photons towards the
       | Earth, at the receiving end how are we recognizing which photons
       | are coming from Voyager and how is the "signal" decoded?
        
         | RachelF wrote:
         | Two main reasons for recognizing the photons: They have a
         | specific frequency, 8.3GHz in this example. It's like tuning an
         | FM radio to a station. The photons are coming from a specific
         | direction.
         | 
         | As to how they are decoded, you'll need to understand some
         | modulation techniques.
        
       | RachelF wrote:
       | What is equally impressive is the number of photons received from
       | radar imaging of asteroids.
       | 
       | They are closer, but the radar equation received power is
       | inversely proportional to range to the fourth power, not range
       | squared as with Voyager.
       | 
       | Anything proportional to 1/R^4 degrades very quickly.
        
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