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If a planet nearly identical to Earth were orbiting a nearby star, how obvious would it be to us, using our current efforts to search for signs of life? Would it stick out like a sore thumb? Or would it be subtle/difficult to detect?

Let's assume we're conducting this search from the Earth or near-earth orbit or by using a probe that remains within our solar system using techniques and technologies that are actually being employed today. In other words, imagine one of our current search efforts happens to catch a glimpse of an earth-like planet. Let's also assume that the other planet is essentially identical to Earth in all its detectable characteristics, with all its life, people, artificial lighting, atmospheric emissions, rocket launches, artificial satellites, radio transmissions, etc. And let's assume that by "nearby" we mean roughly where Proxima Centauri b is, about ~4.2 light-years away.

What particular aspect of this other planet would be most obvious or prominent to us? For example, might we most easily notice patterns in its radio transmissions? Or might we most easily notice bio-indicator chemicals in the atmosphere with spectral analysis?

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The predicate of "roughly where Proxima Centauri b is" is a bit problematic. Anything orbiting a star with activity so violent as Proxima is automatically disqualified - the range of temperatures between calm periods and flares would be wild and automatically made any planet dissimilar to Earth on that basis alone. Barnard's star would be a better starting point.

But let's assume, hypothetically, we have a Sun-like star within similar range. We can find its exoplanets and their orbital radii without great difficulty. Knowing the orbital radius and the star's temperature and size, we can estimate the irradiation the planet experiences and get the likely range of temperatures. If the planet has a moon (or a couple) determining its mass becomes easy - without that, it's a good bit more tricky but still doable, with a considerable margin of error though.

Next comes the spectral analysis of its atmosphere. Water makes it promising. Stuff like what Venus has - sulfuric acid, extremely dense CO2, or a methane atmosphere like Titan - disqualifying. If it has a significant amount of oxygen, that's a "Wow!" moment, and a lot of excitement, because it has a very good chance to host life - but a planet doesn't have to have life to be in major part Earth-like. So, two options:

  1. lifeless Earth-like.

It will be very unlikely to have free atmospheric oxygen, but given the right temperatures, pressures, at least somewhat similar gravity, and enough water, it could be turned habitable with technology we have today (save for getting there, that one's still nowhere near doable). Determining all the factors would take a lot of work and the results wouldn't be certain at all. Plus there are scenarios where oxygen (and water) atmosphere can form without life. (and of course in the unlikely scenario the oxygen formed by these alternate methods, that doesn't disqualify the planet from being a 'lifeless Earth-like' and can be quite a boon.

  1. Planet with carbon-based life.

Atmospheric oxygen, while not an automatic proof, is a strong indicator of life. Finding signs of carbon-based life would take a lot of work, but with the hype around such a promising candidate, resources for that work would materialize quickly. And if we find the planet hosts life, knowing that chances of Earth-like life on non-Earth-like planets are rather dim, we can assume it's very much Earth-like.

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    $\begingroup$ It sounds like you're saying that during our spectral analysis of the other-earth's atmosphere it would be strikingly obvious that: a) it has the right temperature, b) it has water, and c) it has a significant amount of oxygen. Which together make a "wow" moment (becomes an object of extreme interest) but do not actually confirm life. And we would have to go out of our way to conduct more detailed investigations to find other life indicators (wouldn't be obvious from existing search data) Am I following correctly? $\endgroup$
    – Wyck
    May 31, 2023 at 13:58
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    $\begingroup$ @Wyck Precise surface temperature is a bit tricky - as well as a good estimation of ground level pressure. It's quite easy to get a rough ballpark of these, and immediately disqualify a planet way outside the bracket, but the range at which there's liquid water on the surface is awfully tight, and finding whether the planet fits within it is hard and error-prone. But water+oxygen and no immediate red flags (problem size, ballpark temperature or pressure way out of range, problem gases in the atmosphere, etc) are enough to generate that "wow". $\endgroup$
    – SF.
    May 31, 2023 at 14:17
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    $\begingroup$ I really appreciate your feedback about "roughly where Proxima Centauri b is" being problematic. (That part should probably have been a comment on the question, rather than part of your answer) I was just trying to limit the scope to it being close to us. "let's assume it's among the closest stars", or perhaps "about 20 light-years away" would have been a better way to set context? (That puts it among the 100-closest stars.) $\endgroup$
    – Wyck
    May 31, 2023 at 14:46
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    $\begingroup$ @wyck I think it's valuable as a showcase of how you can immediately disqualify an entire system without even checking if it has any exoplanets. All these final analyses that might lead to the final confirmation are only the last step after lots and lots of sifting through lots of obviously non-viable planets. Let's just say, if such planet was within 20ly from us, it would have been discovered by now. $\endgroup$
    – SF.
    May 31, 2023 at 15:49
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    $\begingroup$ @antlersoft You really should ask this at astronomy.stackexchange.com - it's only tangentially relevant to this site, they are the right one to get a really in-depth and authoritative answer (e.g. it's likely quite a few things I said here are significantly outdated) $\endgroup$
    – SF.
    Jun 1, 2023 at 14:51
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The vast majority of earth-sized planets orbiting sun-like stars at earth-like distances would be impossible to detect with current technology even if the host star was relatively close to us. The fact that we've managed to observe any at all indicates that they are remarkably common, so there may be an earth-twin quite nearby that we have no idea exists.

There are two primary means of detecting exoplanets: observing eclipses of the host stars, and observing radial velocity changes as the host star is tugged by the exoplanet.

With our advanced photometric space probes eclipses can be observed relatively easily and for quite distant stars. The problem for earth-like planets and sun-like stars is that the ecliptic plane has to line up very precisely (approximately 0.5 degrees) with our line-of-sight for an eclipse to be visible (automatically excluding more than 99% of this type of exoplanet), and that an eclipse has to be observed multiple times to confirm the existence of an exoplanet. If the exoplanet takes ~1 year to orbit its star, it takes years of continuous observation of that star to confirm the exoplanets existence and orbital characteristics.

The second principal way to detect exoplanets is by using extremely precise spectrographic measurements to measure the change in the host star's line-of-sight velocity caused by its motion around the common center-of-gravity of the star and exoplanet. This method is more forgiving for line-of-sight alignment than the eclipses (although if the orbital plane is perpendicular to the line of sight, there will be of course no radial velocity change). The problem here is that sun-like stars are so much more massive than earth-like planets that the maximum radial velocity change to be observed is on the order of 10 cm/sec, much less than the 1 m/sec capability of the most precise current measurements (https://arxiv.org/abs/1602.07939).

Both methods are much more readily able to detect habitable-zone exoplanets around stars much smaller than the sun-- where the habitable zone demands that the exoplanets orbit closer, with more frequent eclipses and larger radial velocity changes. The most earth-like planets, which would be ones orbiting around sun-like stars in the habitable zone, are all but invisible to our current methods of detection. There could be some around the closest sun-like stars and we would have no idea.

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    $\begingroup$ It is my understanding that SETI is merely looking for radio signals and is neither measuring transits, nor star wobble, nor doppler shift. Would another Earth not stand out as a radio source to SETI searches? Or perhaps Earth-like transmissions are far too low power to detect from such a distance? $\endgroup$
    – Wyck
    Jun 1, 2023 at 16:51
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    $\begingroup$ @Wyck: that would require a civilization broadcasting high-power radio signals, not merely life. Note how within billions of years in Earth history, there was a period of only about 70 years when we were broadcasting strongly enough some distant planet's Arecibo style antennas could hear us. Nowadays, with digital signals with built-in error correction and energy-saving mobile devices our EM footprint dwindled massively. Chance to hit the ~70 year period of any distant civilization is next to none. $\endgroup$
    – SF.
    Jun 1, 2023 at 23:14
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    $\begingroup$ @SF. To quantify to what degree our EM footprint is (as you may allege) virtually undetectable compared to the oxygen in our atmosphere is exactly the kind detail I'm looking for in an answer. It's useful to know that if a SETI search were pointed right at another earth, that it wouldn't be able to distinguish it from noise because earth's EM footprint is miniscule. I just don't know if that's true, which is why I'm asking. $\endgroup$
    – Wyck
    Jun 2, 2023 at 1:43
  • $\begingroup$ @Wyck Primarily, we can't estimate capabilities of civilization much more advanced than ours. It might have much better EM detection capacity, and could send a "Hello" at high power in our direction on purpose - it's not like we're unable to produce high-strength radio signals, we just don't have a good reason to. It may have a kind of technology we know nothing about, that requires high-strength emissions. It might have moved past the limitations of carbon biology and need for oxygen, and won't have a chemical signature we recognize. $\endgroup$
    – SF.
    Jun 2, 2023 at 9:16
  • $\begingroup$ ...in short, we know how to look for non-sapient life pretty well. We only have very vague and very possibly incorrect ideas how to look for alien civilizations though. Most of our ideas are revolving around "if they are like us, how would they (X)...?" which is a very precarious predicate. $\endgroup$
    – SF.
    Jun 2, 2023 at 9:22
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This answer is offered as partially addressing the question, however imperfect this answer may be. The proposed question is very interesting but the attempt to answer is fraught with logical dilemmas. We are asked to assume the planet in question is essentially identical to earth in the advancement of its technological development, and then determine what particular aspect of this planet would be most prominent or obvious to us if observed at several light-years distance. Our means of observation is with an highly advanced observational probe that is located within the solar system, which for the purposes of this discussion, will be considered as parked in a relatively quiet environment deep within the Kuiper belt. We are to assume this observed planet is within a star system that is nearby, but given the characteristics of the planet being observed, we could well be observing earth with the query how would we recognize earth has intelligent life?

For this planet, we are asked -

...might we most easily notice patterns in its radio transmissions (or, if not) might we most easily notice bio-indicator chemicals in the atmosphere...

In general, the answer to these questions is no. But let's assume for a moment that we have been able to observe something telling about this planet. We are challenged to determine the implications of a) the question that is being asked, and of b) the evidence we have found.

In considering this question, we must be careful that we are not establishing the premise of our answer based on notions of things or aspects that are currently present in our everyday technological environment. The only exceptions might be principles of function. For instance, we cannot presume the people of this observed planet have a notion of the passage of time, even though they, as we, understand the presence of time. An interesting way to view the evidence would be to ask, for instance, about the people of this planet and what we could possibly know about them. If we take technology, for instance, all we could say is that if we hear their radio transmissions, they understand radio and have achieved the ability to develop technology. Regarding size of their technological elements, for instance, we could say the physical size of their computational platforms is likely not huge. Further, that these people are likely not huge. But nevertheless, neither can we say that any life form reaching this state of technological advancement has likely undergone a path of evolution parallel to ours even though parallel evolution would almost certainly lead to intelligent life and the development of technology. An error would be to think they look like us, but there may be inferred similarities. For instance, to reach a technologically advanced state, they would have evolved with an anatomy compatible with the manipulation of technological tools and elements, and the assembly of complex and wonderful technological devices. Those tasks require intelligence of some sort, and dexterity. Think about our ability to use a screw driver or pliers, for instance, or in an advanced state of technology, use of photo lithography in development and assembly of miniaturized, large-scale electronic circuits.

Considering the development of civilization and technology, the practical consideration is this: During the 6 billion year history of the planet earth, the window in time for development of our own nascent state of technology has been most exceedingly small, say, much less than just the last 250 years. And earth has undergone 6 mass extinctions in just the last half billion years of that 6 bln year history. Considering the chances of an encounter with a civilization at, or during, this short and most recent 250 year span, given the vastness of time over which this life form has evolved to a civilized state, the unknown age and state of evolution of this advanced life, the evident limitations and exceedingly small probable occurrence of such life on planets within habitable systems in the galaxy, and the expansively vast size of the galaxy, we can see that a chance encounter with another civilization within the time period of this nascent 250-year period of technological development is essentially and virtually non-existent both temporally and spatially. Consequently, the technological advancement of the supposed civilization we have detected may be assumed to be much older and far more advanced than ours, in fact much older by many tens of thousands or hundreds of thousands of years, or even millions of years, if not older. Because this is so, we would not recognize any technology they may have. We may detect the possibility of their presence by evidence within the chemical composition of their atmosphere, and if we detect their radio transmissions, given our total inability to understand their technology, we would find those radio transmissions exceedingly strange and heretofore unknown. Let's step back and consider this again, but from a different vantage.

So what exactly would we see with our advanced observational platform, looking at them from, say, 1.2 parsecs. Atmosphere: hydrogen, oxygen, some carbon, nitrogen. Composition: water, carbon-dioxide, trace methane. Radio transmissions, none, except as those possibly noted within the quiet zone in the vicinity of the 21-cm hydrogen-emission band. What is so special about 21-cm vicinal radio transmissions? For the most part, planetary atmospheres, and to a large extent, all other galactic radio noise, will block or obliterate radio emissions well below the hydrogen radio-emission wavelength of 21 cm. However, planetary atmospheres like ours, are transparent to, and galactic radio emissions are absent from, the quiet radio window surrounding the 21-cm hydrogen radio emission. Consequently, if this planet has an active civilization, and they use radio, we may detect some of their radio transmissions within the vicinity of the 21-cm hydrogen emission. In fact, we benefit from absence of noise for transmissions within this quiescent radio region. Think GPS, for instance.

What would these transmissions sound like? Well, of course, we have no idea. However, regarding radio transmissions, considering the state of our technology in radio, and assuming their state of technology in radio is similar to ours (even though more advanced), we may be able to hazard a guess regarding their uses for radio within the 21-cm band. How would we know what the state of their radio technology would be? Again, of course, we would have no idea, but the principles of radio have been sufficiently investigated and well understood over the time that radio technology has been developed on earth, that we can say our radio technology is as good as theirs except for innovative advancements they have which we have not considered or are unknown to us. Like the principles of physics, the principles of radio have been sufficiently explored and understood that our state of technology is sufficient to be equivalent to their state of technology in many ways, even though ours may seem archaic or primitive or ancient in comparison to theirs, and missing advanced technological elements. The point is this: If they incur radio emissions within a quiet area of the radio spectrum, then at 1.2 parsecs we will easily be able to hear them, otherwise if they are transmitting radio that we cannot hear, their radio transmissions are so soft they cannot be heard or they are transmitting within a noisy part of the radio spectrum. Consequently, without radio, or our ability to hear them, they would be undetectable. Our search would move on.

So here is the kicker: If we were to hear radio transmissions from this planet, how would we know what they are? Further, we will certainly find we have no way to understand what they are. All we could surmise would be that their radio transmissions are not frivolity, but rather are carrying real information of some sort, even though we cannot determine what that information would be. Keep in mind, if we cannot establish the premise of our observations based on notions of things or aspects currently present in our everyday technological environment, including language, then we would also not have the ability to understand these radio transmissions, even those from earth, if, in fact, earth was the planet we were observing.

For additional context, see my answer regarding the Fermi paradox, here.

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