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The answer is to limit transmit power, but there's some real questions as to the feasibility of this as an approach to learn a language.

The simple answer is that the Americas have radio, but not large power production systems. Consider that a small walkie talkie can operate on a pair of AAs, and a radio reciever can also operate on a pair of AAs. However, the radio station transmitters are measured in megawatts. If such localized power is simply not feasible with the way the American technology progressed, then they can't transmit. Perhaps their society valued efficiency over brute strength.

However, I do have to point out a major hurdle for your idea: the Americans probably can't learn English this way. You can't learn a language passively without some shared context. The only thing they could talk about is the weather, and for the most part the weather is very different half way across the globe. Perhaps the Americans might learn the words for the seasons, because both parties are in the northern hemisphere, but this would probably be the limit.

Consider if you had a message like this:

Uvtu cbjre trarengbef ner znpuvarf.

Now you've spent a great deal of time analyzing this langue. You understand the grammar petty well. You understand that if a sentence has the word "ner" in it, it describes something that has some transitive behaviors. You've seen "Znpuvarf ner gbbyf" and "znpuvarf" is on the right side of "ner" in our sentence, so you think it's highly likely that "Uvtu cbjre trarengbef ner gbbyf" would also be a true sentence. Unfortunately you don't have any context to know for sure.

But how could you possibly know that "znpuvarf" was the word the Europeans used for machines? You never got to see one, and you never got to ask the Europeans questions. You need something like the Rosetta Stone to stand a chance of getting the meanings right.

And I'm being kind here. The sentence structure I used for the language in this example is very similar to English. The meanings of the words are also similar. We don't have issues such as the Chinese word "Ch'i," which is brutal to try to capture in English.

In fact, all I did was rot13 encode English to create that language. If you knew English, and I gave you a large enough text, you'd have eventually realized that all I was doing was letter substititions. However, if you didn't already know English, it would have been inpenetrable.

Languages are designed to be used in a common context, such as face to face communication. It is, in fact, mathematically provable that you cannot determine whether a sentence is true or not by doing nothing more than listen to sentences.

It's not until you're face to face with your newfound friend, and someone does something terribly foolish in a cute sort of way, and that friend points and exclaims "baka!" that you stand a chance of understanding what "baka" means.

(In this case, "baka" is not rot13. It's actually a Japanese word which is terribly frustrating to try to properly translate into English. "Fool" is a decently close word, but it misses out on key nuances)

For a wonderful depiction of what happens when you lack proper context, I highly recommend the movie Galaxy Quest. In it, they have an alien species which passively observed our Star Trek like TV show, and then tried to interact with us based on those observations. Hilarity ensues, and they don't even try to approach this language question. It's the engineering that goes horribly wrong when they build their Star Trek like ship.

Edit Reading the comments has been fascinating. It appears this task is less clearly impossible than I had thought. HAM radio operators demonstrate the ability to connect across the globe with very low power, though such connections are spurious. This suggests that transmission may be possible, but they might not find it valuable because they can't control the environment enough to maintain a reliable connection to one individual over long periods.

The second interesting tidbit was finding out that AIs were having great success in identifying words which have the same semantic meaning in two language without an interactive back-and-forth pattern or parallel sentences.
This would make it possible to identify, for instance, the word for "leaf" and "tree" by using their relationships.

I still believe the Native Americans here could not achieve this. At the very least, it would require a robust computer hardware production capability, which is at odds with the "low power" argument. However, it does show there's a sliver of hope. It's possible, though I'd still argue improbable.

Thanks for the comments, all!

There are other potential issues with your scenario, such as CrossRoads brings up in another answer. If I recall, the Germans actually tried to see if the English were using radar technology in World War 1, but they were not checking in the same band that the English were transmitting, so their engineers reported back that their enemies were not using radar technology yet.

But you suggest this is a modern (or at least closer to it) time and technology, so I will ignore the other issues for a moment and just assume that both sides have some radio capability and that they either randomly happen to be using the same frequency ranges or that they are tuning into ranges they've found each other to be using (like SETI searches/tunes to other stars looking for life)...

The answer to you question is that, yes, you can have the ability to receive without having the ability to transmit. There could be multiple reasons for that, and any 1 or more of them could be thwarting your Americans simultaneously.

• Transmitting takes more power. This is my favorite for you, as all you have to do is say that the Americans don't have the ability to transmit all the way across the ocean. That is easier than saying they cannot transmit at all.




• The signals can be highly directional. This is related to power, but it deserves its own mention. Maybe the Europeans figured out earlier how to send directional signals so that they could send at reduced power.




• Though the physics behind transmitting and receiving is similar, and you can use the same antenna to do both, the hardware to send and receive need not be the same. You can make one without having the other.




• Did the Americans even make it themselves? If you want to keep to history and say that the Europeans were technologically a bit more advanced, you could have the Americans find a European radio receiver washed up on shore.




• Maybe the Americans don't even have an electrical power source at all. Maybe they just stumbled onto a way to passively collect the signals and don't even understand how it works. Picture a cartoonish funny-looking huge receiver connected to the good old string and cup telephone method.




• The list could go on, but the point is yes, there are many ways that the Americans would be able to hear the European broadcasts but either not be able to broadcast back or at least not have the Europeans be able to receive the broadcasts back.




• Here is another possibly realistic one: the Americans have developed more sophisticated radio technology, but the Europeans have developed better power technology. This also helps with the "but they're probably not on the same channel" arguments. Let's say the Americans have developed radio technology that lets them scan and search for intelligent life on other planets continents, but their electrical power technology is much more limited. The Europeans have developed powerful batteries or other means of pumping a lot of power through their very limited radios. If the Americans transmit with very low power and/or Europeans have not developed good amplifiers, then in this scenario too you can get what you want. Though the Americans can probably transmit over very short distances in this one.

Another argument against the "they aren't going to be on the same frequency" challenge is this: we use very narrow frequency ranges for communications now, but that was not always the case. The ranges used to be a lot wider. Before techniques were developed for tuning into a specific frequency, receivers would be receiving across an entire large band. If the transmit and receive devices are both operating on very, very loose bands, the likelihood they will overlap is greatly increased. If they have the technology to limit themselves to narrow bands, then they probably also have the tech to scan over the band and look for communications.

OP did not specify what level of technology this is, only that there are radio communications. And OP should not need to specify that, especially since there is no science-based tag. It is sufficient to say "They have the tech to do this, but not that," and to change their mind to suit the needs of the world building.

How is it possible to capture long distance radio transmissions without the ability to transmit it back?

By just having a radio receiver. Lots of people only have radio receivers.

Is it feasible?

Definitely not. No one just invents just a radio receiver, if for no other reason than you can't test your receiver without having a transmitter.

Even if you develop a receiver that -- through wildly dumb luck -- just happens to be on the same frequency that Europeans are transmitting on, no inventor worth his salt is going to just stop there. His first thought will be, "how do I transmit back?"

EDIT: specifically, anyone smart enough to have knowledge of EMF and invent a receiver will be smart enough to (quickly) build a transmitter.

Perhaps its an accidental receiver?

Many of us have heard stories about people picking up radio broadcasts like baseball games on their tooth fillings or dental braces. Perhaps some type of jewelry or adornment worn by the Americans works the same way. They don't quite yet understand how it works, but they can duplicate the item's construction, and even tweak it a bit to improve reception.

The only reason I can conceive of that a civilization would develop receiver radio technology, and no transmitter would be some form of radio telescope.

As others have pointed out, its highly unlikely someone would stop there, and not try to figure out how to generate the signals; but if for some reason someone made a Foxhole Radio, you could find a creative way to hand-wave it.

What about an European ship lost at high seas, that somehow ends up on American coast with just a few survivors after months of starvation?

The ship would carry a radio receiver but the transmitter would have been broken or doesn't carry very far. The few survivors could help the native Americans get started in English language, which they could then better learn more about using the radio.

If it is important for the story, the few survivors could later die and fall into obscurity, while more radio receivers could be manufactured if they had some electronics knowledge to start with.

This topic

https://ham.stackexchange.com/questions/574/what-bands-and-modes-will-give-me-voice-at-3-000-miles

makes that seem pretty unlikely without some coordination between the 2 sides as to frequency to be used. Also the hardware needed is not something one could just throw together.

If you really want voice to anywhere in the world, you'll want a huge yagi antenna on a large tower, transmitting at the full legal power in a quiet RF area. Other than that, you will have some compromise

Yes. It could be possible. With some assumptions.

You don´t need advanced technology to build a receiver. Perhaps even some of you built at school a "Crystal Radio". It is an AM receiver. It uses only the power of the received radio signal to produce sound, needing no external power (no batteries, no plug). It is named for its most important component, a crystal detector, originally made from a piece of crystalline mineral such as galena. (This component is now called a diode).

The complete description is here: https://en.wikipedia.org/wiki/Crystal_radio

So, to make America able receive the signal, you need to find out a "reason" for them to have built something like this. Perhaps they were trying to build another type of machine for some other thing, and suddenly the "thing" started to talk in strange languages.

Although they don´t need to have developed radiocommunications, some technology will be neded (they need wire and a coil). And finally they need a way to listen (earphones). Piezoelectric earphones could be theoretically used if they have not developed their electromagnetic science enough.

Looking at current tech - we have wind-up emergency radios that can be powered by cranking.

What's to stop a container of them washing up on the America's shore? Downside is they're normally fairly short-range FM radios and are unlikely to receive local FM broadcasts from Europe or Africa.

Then lets say the transmitter culture has no particular power restrictions and has powerful transmitters capable of going a lot further.

OR how about a set of crank-powered shortwave radios getting washed up? Something a survivalist might have? https://www.ambientweather.com/kakahacrsopo.html#caption is capable of AM/FM/SW1/SW2 reception.

This could be seen as "deus ex machina" where the answer just comes from the sidestage and will distract from your plot.

Theres more to making a radio than the sum of its parts

Without prior communication, the Native Americans would need to have developed radio independently.

However, to make a radio you need a fundamental understanding of magnetism, electromagnetism, conductors, capacitors, sound, and perhaps even integrated circuits. To get these you need metallurgy, refinement and mining.

None of the above would be possible without the steady education and scientific rigour established in an Enlightenment, when scientific principles began trumping superstitious ones.

Even means of production would need to match - with experimentation coming from the constant bouncing of ideas in a scholarly manner in cities, and for this the cities need to be stable, large enough for a population to exist free from hunter-gatherer tasks. Which also means you need institutions established to promote cities, farming, engineering and sewerage, water distribution, waste disposal. To develop these, you need a sophisticated writing system to transmit knowledge, including also an understanding of mathematics.

These all go hand-in-hand with the development of science and education, leading after a long process, eventually to the creation of a radio.

If the above happened than it is equally likely the Native Americans would be as advanced as the Europeans - likely to that the would have travelled extensively too. They may even be teaching Europeans a thing or two.

The Two Go Hand In Hand, Scientifically

Generally speaking, the scientific background knowledge required to build a receiver is the same as for a transmitter. It is not really believable that someone could do one and not the other. At least, not for long.

High-power, noise-free transmission, however, is very difficult to achieve. In practical terms, your choice is between disparity in power generation or ignorance of radio/electromagnetism.

Near-equivalent radio tech

Radio transmission requires power, and the power level increases dramatically with the distance you intend to transmit.

It is entirely possible that your European broadcasters are pushing hundreds of watts, or even kilowatts. In the right bands, those signals could be received around the world.

Your American natives could have the exact same radio tech---and even communicate with each other via radio---but still lack the power required to respond to the Europeans.

A radio would need far more power to transmit overseas than to receive. A modern radio needs only ~5W to receive and power its speaker (and some work with less), but it could output 100W+ broadcasts and still not be heard overseas.

Technological disparity

The Americans could have a primitive device they built, or they could have a European device which they do not fully understand.

It is possible that the natives' European-built radio was acquired via theft, trade, or salvage. Perhaps it is damaged and cannot transmit.

They could even have a device capable of communicating with Europe and just not know it. Maybe they're held back by nothing more than the flip of a switch or the press of a button.

http://www.arcsandsparks.com/aboutcrystalradios.html

Radio receivers can be very, very simple. A badly done dental filling can end up making one out of one of your teeth and suddenly there are voices that only you can hear.

A crude crystal receiver could easily be accidentally created as a piece of artwork if both an amplifying crystal and a piezoelectric crystal were part of a wire sculpture and things got wrapped in just the right way. (Teeth are both, hence why a bad filling can make a radio.) From there add some tinkering to make it work better and they could conceivably end up with decent receivers.

The North American groups didn't really attain the level of technology where it would be likely to do this, but several of the South American tribes did, and even had what appear to be primitive acid batteries in some of their ruined temples, though what they used them for we don't actually know for sure. Had there been intelligible transmissions at the time they might well have stumbled upon a receiver at some point.

The amount of power necessary to transmit that far would likely be prohibitively expensive for the Europeans of the time though and learning a language with no reference context is rather impossible, so that will be your big problem... but I have run across theories that South America may have been visited by the ancient Greeks and/or Romans at some point, so if your transmissions were in Latin there's a tiny possibility that someone on the receiving end might understand them. But you'll still need a reason for the Europeans to be running megawatt transmitters when kilowatt ones would serve their needs perfectly well... Maybe they're communicating with colonies in Africa?

Honestly, I don't think the above scenario is feasible.

The Native Americans could not know about these transmissions from Europe without having the means to receive them. This means that they would have, for unrelated reasons, developed radio technology independent of the Europeans.

Moving on, why would they develop a device that could receive but not send transmissions? I simply can not think of a practical purpose for this.

And so if they had developed radio technology they would almost certainly have the means to send AND receive the transmissions and they would be able to reply to the Europeans.

Maybe a scenario where the Native Americans for some reason (religious or otherwise) decided not to reply to the radio transmissions that they had received would work better.

I recall an old Radio Shack kit that was a very simple crystal AM receiver. I had it as a kid, though I don't recall if I ever got it to work very well, but it certainly was simple enough and needed no outside power, or not much.

In any case, in aviation, we use receive-only radios for a lot, including navigation and weather. Even some communication is done with split radios using one object, like a navigation station, to receive, and a completely separate channel to transmit.

The biggest problem I see with the OP's presentation is creating a receiver that operates on the correct frequencies being transmitted, and suitably notching the correct frequency or otherwise suppressing spurious noise and transmissions, to make the intended transmission intelligible.

Would they really want to transmit back ?

It is straightforward to find transmitters using radio direction finding methods.

If for example SETI found signs of extraterrestrial life, would you really want to send a signal to them to meet us ? (to invite them to take our resources etc. ?).

Another idea: in the movie 'Galaxy Quest', extraterrestrials see our daily TV transmissions as 'historical documents' since their civilisation is much more advanced. Probably it was quite amusing for them but as far as I remember they did not see a need for communication or visit for a long time.