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Sorry if this is not the right question for this channel, I just need to know and there is no good place to ask.

It is said the Fine Structure Constant α is one of the most fundamental constants in nature. Unlike the likes of the speed of light, α is dimensionless. I have heard an argument that when we encounter intelligent aliens sending the α at them is the best way to let them know how much we know. It was said that we should of course send the constant in the binary numeral system.

My question is: how do you communicate a fraction (α = roughly 1/137) in binary so that even aliens can decode it?

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    $\begingroup$ I’m voting to close this question because it is probably more suited to Worldbuilding and is not really an astronomy question. $\endgroup$ – StephenG Dec 16 '20 at 2:56
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    $\begingroup$ @StephenG "more suited" is never a close reason. We only vote to close if we think it is off topic here. OP decides where to ask, moderators decide where to migrate. voting to keep open! $\endgroup$ – uhoh Dec 16 '20 at 6:13
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    $\begingroup$ I feel this is not particularly an astronomy question but more about agreeing communications protocols with a hypothetical unknown (and possibly unknowable) entity. In any case, I suspect this is going to be highly opinion-based and as written it covers an extremely broad area (communication protocol, equipment, target selection, etc.). $\endgroup$ – user24157 Dec 16 '20 at 7:27
  • $\begingroup$ As bits. In base-2. Or, sending 137 single thing. $\endgroup$ – peterh Dec 16 '20 at 8:40
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Send two pulses of whatever (light, radio) you are using for communication, one a factor of $\alpha$ longer than the other.

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    $\begingroup$ That strikes me as really inefficient and unlikely to work. Absorption and scattering in the interstellar medium varies with wavelength, and not all wavelengths are equally easy/hard to produce, which is a significant concern when you're already using massive amounts of power just to transmit a detectable signal at optimum wavelengths. Plus how would the aliens know to look at either signal? Even if one is on the objective optimal band, now you've gotta hope the aliens are thinking the same thing you are and monitor both the $\alpha$ and $1/\alpha$ wavelengths. $\endgroup$ – zibadawa timmy Dec 16 '20 at 0:57
  • $\begingroup$ How about continuous transmission on two nearby frequencies with $\frac{\Delta f}{f} = \alpha$? or $\frac{\Delta \lambda}{\lambda} = \alpha$ or $f_+/f_- = 1+\alpha$ or... $\endgroup$ – uhoh Dec 16 '20 at 2:12
  • $\begingroup$ I meant longer pulse, not longer wavelength. So an alternation of (say) 1 minute and 137+ minute pulses with a suitable gap in between. $\endgroup$ – Steve Linton Dec 16 '20 at 14:21
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We've already attempted to communicate with aliens (and I don't mean teenagers), notably using Voyager 1 and 2 and their "gold records". Any intelligent technological civilization should easy decode it (although I'm not sure what they could usefully make of the audio). Communicating a number is easy - finding aliens is the tricky part. :-)

I have heard an argument that when we encounter intelligent aliens sending the α at them is the best way to let them know how much we know.

This is entirely dependent on how far apart we are. If we've sent a signal or message light years they already have a good idea of our technological level. Working out the fine structure constant is not really difficult. They'd be much more impressed by us sending a message over such a distance (or maybe not if they consider whatever method we use as primitive).

But if we're communicating over those distances then, courtesy of the limitation of the speed of light, we're not going to be telling them what we know, but one small part of what we knew when we sent the message.

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