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Imagine there are two regions, one of which has a significantly higher level of radiation. Think of Pripyat (higher level of radiation) and its surroundings (lower levels).

How can a person without equipment and without education in physics (but with a curious mind, good memory and analytic abilities) learn that there is such thing as radiation?

Let's assume he or she is immune to it and can walk around both regions without dying for decades.

Obvious ways:

  1. He or she feels worse after a visit to the contaminated region.
  2. The plants are bigger in the contaminated region.
  3. In the contaminated regions there are animals, which look differently due to DNA modified by radiation.
  4. His fellow people get sick, when they bring items (e. g. stones, metals) from contaminated regions in their homes, or put artifacts made of those materials close to their body. E. g. when a person puts a ring made of contaminated metal, there is a discoloration on his or her finger.

Antyhing else?

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    $\begingroup$ Do they have photographic film? Because that's how radioactivity was first discovered in our world. Maybe in your world, they try to make photos, and find that they can't successfully photograph anything in Pripyat because the photographic film always gets black when you bring it there. $\endgroup$ – celtschk Sep 12 '15 at 11:28
  • $\begingroup$ Also there might be some naturally occurring materials displaying radioluminescence. Those materials might then glow in Pripyat. $\endgroup$ – celtschk Sep 12 '15 at 11:42
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    $\begingroup$ Are you sure that your obvious ways are science-based? I'm not an expert in radiations but I think your observations are wrong. In order to feel bad, you need a high dose of radiation. 1: Staying for long in Pripyat increase the risk of certain disease like cancer but that is as bad as it get unless your close to the source of radiation. You won't grow tentacles 2: Maybe but the vegetation grew because it was abandoned, not because of radiations. 3: The modification (like cancer) are very hard to see just by looking at them unless you make some sort of medical examination. $\endgroup$ – Vincent Sep 12 '15 at 15:21
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    $\begingroup$ Simple diffusion cloud chamber, you need alcohol and something to keep it cool. Cheers!🍺 $\endgroup$ – user6760 Sep 13 '15 at 2:23
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    $\begingroup$ Astronauts report that when they close their eyes they see random flashes of light. This is caused by certain types of radiation hitting the retina. $\endgroup$ – Donald Hobson May 13 '16 at 18:46
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Make it a "Radi-sense", or a special feeling that let's him know when radiation fields are higher than normal.

Possible Solutions

Since this is guy is immune to radiation, then it's plausible to assume that he has consumed some heavy metals without ill effect. Growing new organs isn't plausible, since this is science based, he will need to use existing body structures. Absorbing radiation often causes heat which can be picked up by heat sensing nerve endings. So with a small concentration of the right metal in the right place in his body, he will be able to detect some kinds of radiation. If his whole body gets warm, then he knows it's just warm air. If the special spot gets hotter than ambient then he knows it's radiation.

No help from Evolution

As he is immune to the levels of radiation in Pripyat, there's no evolutionary pressures to develop a rad level detection ability. Also, this is the lifetime of one guy so evolution can't help him.

Technology isn't much help either

In a post-apocalyptic scenario, the economy has collapsed so building rad detection equipment even with the requisite expertise will be very difficult. Without expertise, it's impossible.

If he's immune to radiation then there's no really compelling reason for him to detect it. It would be like us being able to detect nitrogen concentrations in water.

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In the real world, radioactivity was discovered in 1896 when Henri Becquerel tested uranium for X-rays. It left an impression on the photographic plates, but these rays could be bent by a magnetic field while X-rays could not.

The basic principle behind photographic plates was actually discovered in 1717 by Johann Schulze, who mixed chalk, nitric acid, and a small amount of silver to make a silver nitrate compound that would darken on exposure to light. As a demonstration he would fill bottles with this "liquid film" and hold them under a stencil in direct sunlight. This left black marks on the surface of the liquid, which were detailed enough to make readable words.

So perhaps in your world a scientist made a discovery similar to Schulze's, and was sending a number of bottles of "film" to a colleague in a different city. The bottles were sealed in a lightproof box to keep them from becoming overexposed. But when they were carried through an area with a very large amount of natural radiation, the "film" darkened for no apparent reason. They might have refined the liquid film further, eventually creating one sensitive enough that it was exposed on arrival when the others hadn't (prompting further investigation). Or maybe they noticed that the especially-sensitive mixture was dark on arrival when sent to one city (on the other side of the affected area) but not another. Further testing revealed that only this one place had the effect, and that some parts were stronger than others. A flask of the nitrate solution under a dark cover became a primitive "radiation detector": look through a peephole to see if it's darkened, shake it to reset the "detector" (by bringing more undeveloped solution to the surface).

This would probably require a LOT of radiation in the affected area. But if it causes noticeable short-term effects in living things, it could be enough.

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Before I start I wish to remind everyone:

While radiation in fiction usually is a strange mix of white and black magic that either make you a super-hero or turn you into a decomposing grotesquery, radiation in real life is not anything like that. Radiation is not different than heat, light, sound, wind or any other force of nature: too much of it will kill you, but it takes a LOT to get there.

Half your bullet list of how he would notice things are different do not apply in real life. No, animals and plants do not grow bigger in radiation. No, animals and plants do not deform or change that makes it any more noticeable beyond normal regional variation in species. If anything, stuff die. That is about the only thing your hero can notice at first glance; that some places appear sterile. The infamous Chernobyl Red Forest is the most classic case of this, and a very rare one at that.

And as far as getting Acute Radiation Sickness, well it would have to be some pretty severe radiation for that to happen. ARS kicks in at about 1000 mSv dose over a short time period (less than 24 hours). This can easily be the case for items, the Goiânia accident for instance demonstrated that. But the sphere of influence there was very localized. Once the source gets spread out over a large area, the intensity quickly diminishes. It is not impossible that an area can give ARS, but the nature of your apocalypse would play a big part here.

Anyway, the core of the question: assuming your hero knows basic physics, physiology and similar, would he discover radiation simply by noticing some items — or being in a specific area — makes him ill?

It is possible, yes.

The Star Trek: The Next Generation episode Thine Own Self shows a possible scenario with Data - suffering memory loss - ending up in a pre-industrial community, using basic science skills and some physics knowledge to deduce the existence of radiation. The radiation is coming from items in that case. It is a bit too long to write out the entire procedure; I recommend reading on the link.

Is this applicable to your scenario? Well it can be. Do note though that in your scenario, your hero would probably cut himself on Occam's Razor first. Since we are essentially talking about discovering what from his perspective actually is black magic — i.e. something completely unknown, invisible, without scent or sound, and that is causing ill health or even death — he is likely to assume other, simpler explanations first, like poisoning or infection. This is because symptoms alone are not enough to differ between ARS and ailments caused by pathogens or poisoning.

You have to let him rule out those things, while still maintaining enough curiosity to keep working with this black magic that is killing stuff and/or making him ill. It is not entirely impossible, like "Thine Own Self" showed, but you do have your work cut out for you. :)

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Maybe they might accidentally make a cloud chamber: https://www.youtube.com/watch?v=OFDV9Kpxfp4

The idea of a cloud chamber dates from the early 1900s: https://en.wikipedia.org/wiki/Cloud_chamber

The cloud chamber, also known as the Wilson chamber, is a particle detector used for detecting ionizing radiation.
In its most basic form, a cloud chamber is a sealed environment containing a supersaturated vapor of water or alcohol. When a charged particle (for example, an alpha or beta particle) interacts with the mixture, the fluid is ionized. The resulting ions act as condensation nuclei, around which a mist will form (because the mixture is on the point of condensation). The high energies of alpha and beta particles mean that a trail is left, due to many ions being produced along the path of the charged particle.

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Electroscope - is extremely simple(two pieces of foil) tool that allows to detect static electricity(that is easy to generate with rubbing wool).

Electroscope discharges in presence of radiation much faster - there where even plans for DIY radiation meters based on that principle during Cold War.

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