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Quick answer:

Some sort of indistinguishable-from-magic force field.

There's no material of which modern materials science is aware that would have the structural and optical properties you're seeking. Diamond, even if it could be made large enough, has terrible shear strength, so being able to resist wind for thousands of years would be insufficient - plus, of course, a suitably determined effort with other diamonds would get through it.

(For that matter, even leaving aside the optical properties, the wall as described is likely to be almost impossible to build - even hypothetical building materials need structural supports and buttressing lest they simply be blown over.)

So the ancients built a force field projector powered by geothermal energy that creates a solid, inch-thick "wall" which leverages physics properties of which we're not aware to create a solid barrier through which only electromagnetic radiation can pass.

There is no material that meets the requirements of being transparent and completely unweatherable, unscratchable etc... over thousands of years. Even diamond isn't that impervious, if you take grandma's ring to a jewellers they will often find a slight chip from daily wear.

Therefore, we need some sci-fi handwaving here. This wall is either made of unobtantium or can self-repair. Each of these stretches physics in uncomfortable ways

Unobtainium

• Go nuts, perhaps define it as an ultra-hard ceramic or a metal of unusual properties.

Self-Repairing

• Automated nanites? How about a diamond wall with Nanites that can recover carbon from the air and insert those atoms into the diamond to maintain a perfect lattice of great optical clarity. Although this suggests an active tech facility that maintains the nanites and, perhaps, atmospheric processing to obtain the carbon.

PS. Not hearing anything through the wall is hard (conduction of sound through a solid is excellent -- cup-on-the-wall type methods would work pretty well). You might need the wall to hum or something to drown out these sounds. Or have an air-gap in the wall that somehow doesn't get filled with snow.

The closest idea I can come up with is sapphire (or other transparent ceramics. It can be clear if made that way, it is a 9 on the hardness scale so unless you scratch a diamond across it it would be very hard to leave marks on, and when properly mixed with other substances during creation things like it can be used in bullet proof windows for armored vehicles (see Aluminum oxynitride which is like sapphire with extra bits).

This coupled with an absurdly high melting point should make it more or less indestructible to medeval civilizations. If you make it thick enough to support being tall enough that nothing goes over it (say ballpark 10m thick at the base with a gentle taper up to 100m) at ground level you may be able to mar it but it is naturally resistant enough that it is doubtful people would be able to seriously damage it without a lot of time, effort, and explosives

though I'll be honest I am not sure the compression strength of sapphire is high enough to support such a tall and dense structure. Maybe have hollow portions higher up to get rid of some of the weight or have opaque materials at regular intervals for supports

To ease the completely unbreakable portion of your description since you are talking about a relic of an advanced civilization it could be that the wall has a method of self repair like a gene tailored bacteria or nanobots that refill any cracks, scratches, etc that might occur.

Time/Space Sheer field

This section of reality is sheered in such a way that the time/space location on the other side is completely different. Even if the two medieval civilisations circumnavigated those mountains, they would only perceive the field from the opposite direction.

The sheering permits photons (massless objects) through but seriously twists, deforms, and even repels mass that reaches a certain point. It would also explain why sound cannot penetrate. The internals of this wall are effectively a vacuum.

As for the power requirements, a civilisation that has time/space sheering knowledge to the ability of this wall, could easily transmit power through a much smaller time/space shear from some astronomical power source such as a neutron star/black hole/etc...

You need a secondary structure, a primary one, and transparent cladding

Modern day skyscrapers are often clad in glass, to form full height glass 'walls'.

This is achieved with what is called a 'curtain walling system'. It is essentially a primary structure, with a secondary structure attached that supports smaller glazed panels. This enables the following advantages:

• The wall is not supported by glass, but instead a protected robust structure behind it.


• The wall is partially flexible, wind loads could slightly bend the wall as the glass is segmented. The secondary structure under could cater for deflection, while the primary structure caters for the main static load.


• The glass could be as thick, strong or rigid as needed, just being accommodated with a thick structure as needed behind it.


• The structure behind can be a truss-like structure, using lightweight steel elements (much like high voltage towers), in particular if you do not require the wall to be habitable. The interior structure has the added advantage that it is protected from weather.


• The primary structure being protected could be large concrete columns, or thick steel columns, as large as is necessary


• The glass could be replaced individually from behind if any damage occurs, some systems have internal fixing frames intended for interior access in case exterior access is not possible.

An example architectural detail of a framed curtain wall:

An example of an alternate frameless, spider joint supported detail, with a secondary structure (primary not shown):

There is theoretically no limit to the height of these structures (as is exemplified in our tall buildings today), with greater size only requiring greater structure behind depending on wind load. Thickness can be increased for longevity if needed, and if there are no economic considerations, increased at whim to last centuries (a lot of existing curtain walling systems have been in existence for a long time with little to no maintenance).

Wind, so the material is air. Natural wind is funneled by a gargantouesque ravine reaching far away and creating the effect you describe. If ever the wind decreases to much (after some extraodinary event) the walls heat and natural fournaces below come into action in contact with water projecting streams of vapor. Water below might also be a carved system of water streams and tanks.

Rock crystal

(Quartz) has the lowest potential for weathering and consequently it is very common as a residual mineral found in veins within sandstone which could have weathered each side , at the head of a mountain pass the rain would wash the sandstone down each side of this cleft between phenomenally steep valley sides thus there are no holes through or around it..

Could be top heavy crystalline the higher it gets since the ancients were mining in from each side, but for whatever reason the hardest transparent core had not been finished and past attempts to climb or dig at it have resulted in shards falling from above, keeping later attempts at bay due to the gods displeasure ?

There's a different problem here.

You have the wall being impossibly high, ridiculously long, impervious to damage, impervious to sound, and perfectly clear. Okay. Let's just take that as given for now.

You say that it's a place where people come for tourism, to communicate via sign language, and (for smallish children) to throw rocks at it. Fine. Then you say that it's across a pass in a mountain range, where the storms are bad enough that no one has ever managed to get over the thing (and also there are terrible beasts). That's a problem. In particular, no one would go there. A pass that's that treacherous is the sort of thing that people only climb to with strong reason, and "gawk at the folks who can be seen but not heard and not touched" isn't a strong reason - especially not since they'll have the same sort of pass on their side, so most days they won't be showing up either.

If you want people to actually interact with this thing more than about once a generation, and if you want them to have any contact with one another through the wall at all, you need to make it reasonably accessible.

If you do that, one of the things you will see, I suspect, is architecture. Having an impossibly tall, smooth wall that won't fall over no matter how much weight you put against it is potentially really useful from an architectural standpoint. The opportunity to leave the glass wall side of your building open, and thus to do socially shocking things where you know that people can see, but they can't possibly inform anyone you care about is just bonus. (Walking about without a hat? Scandalous!)

I see a few comments related to "aluminum" and I recall from Star Trek, the concept of Transparent Aluminum and turns out, has been created. Further reading per the link suggests Iron can also be made transparent - see below:

https://en.wikipedia.org/wiki/List_of_Star_Trek_materials#Transparent_aluminum

Pure transparent aluminum was created as a new state of matter by a team of scientists in 2009. A laser pulse removed an electron from every atom without disrupting the crystalline structure. However, the transparent state lasted for only 40 femtoseconds, until electrons returned to the material.
A group of scientists led by Ralf Röhlsberger at Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany, succeeded in turning iron transparent during research in 2012 to create quantum computers.

Vertical conveyor belt

I've been thinking about some of the objections and have come up with answer to my own question that might work.

Maybe it could even be made of thick glass. The wall could be blocking a tall narrow rectangular cut through the mountains - an artificial pass. The wall could be quite narrow (say enough for ten-abreast to pass through) and thus supported all the way up by a frame.

EDIT - Apologies - I should have made something clear when posing the question. In my imagination the pass is cut through the mountains by the aliens. It looks something like the following only much more smooth-sided and rectangular. The pictures are from the ancient site of Petra. https://en.wikipedia.org/wiki/Siq

https://upload.wikimedia.org/wikipedia/commons/thumb/e/e3/PS-Petra_6148.JPG/1200px-PS-Petra_6148.JPG

https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/V%C3%A4gen_in.jpg/800px-V%C3%A4gen_in.jpg

The wall consists of sheet of material that slowly emerges from a slot at one side of the pass and eventually disappears into a slot on the other side. Behind the scenes, the material is melted and reformed after which it goes through another slot and back to the starting point where the same thing happens. Thus the wall is a kind of continuous vertical conveyor belt whose surface is always being renewed.

Problems

There would have to be a substantial cache (of sand in the case of glass) or other renewable source of wall-material to make up any losses from natural wear-and-tear.

An enormous power source would be required but I suppose it could be nuclear.

This may not be exactly what you described, but one idea could be to use screens/projections on each side.

The "wall" could be built out of regular material, at least on the inside, with some form of ultra-hard glass (or transparent-steel) coating the outside. Each screen then projects a live feed of the other side. To a medieval civilization this would more or less look like a transparent wall, with each side seeing a projection of the other. The display itself could even use some advanced form of e-paper tech in order to avoid backlight issues.

While this can maybe solve some of the issues of material and structure of a solid wall, it does of course pose questions about power supply and wear/tear on the hardware itself. This could be ignored by claiming it uses futuristic self-repairing tech, but it really depends on the setting.

Magnetic Barrier

A very, very, very strong magnetic field would be both entirely transparent and impervious to all materials*. Because it's not a static surface it will always remain perfectly clear as it won't collect dirt or debris.

How does it work? Unlike ferromagnetism, which is a property only exhibited by a few materials, diamagnetism is a property of all materials. Given a strong enough magnetic field everything would be repelled*.

To anyone experimenting with this "wall" it might appear to be soft. As they begin to press against it they would feel increasing push back as the repulsion force builds until they can't press further (which may become painful). Objects thrown again this "wall" would have a slight bounce back.

Sound can also be controlled by magnetism. The "wall" could be deliberately engineered to reflect sound back to its source. However the very nature of such a strong field may perturb the phonons of sound enough to make the "wall" naturally acoustically impermeable.

* Strictly speaking a field strong enough to repel solid objects would only have a weak interaction with sparse substances such as the oxygen and nitrogen in the atmosphere. Perhaps producing a slight wind and/or higher levels of oxygen at the wall. Additionally, photon lensing would be imperceivable at this level.

Relax the definition of "Transparent"

As several other answers have discussed, building a massive, impenetrable wall out of transparent material is impossible. But if the ancients had advanced technology, the same effect can be achieved without the wall actually being transparent in the sense that light passes through unobstructed. Simply cover the wall on all sides with a cloaking device.

In essence, make the whole thing a screen that shows the viewer the light hitting the wall on the opposite side, captured by nanotech cameras or similar. Rudimentary versions of this technology already exist (with varying degrees of success). For fictional ancients with advanced technology, a perfected version that shows the correct image from any viewing angle should be trivial. Cover the screen with a layer of diamond to protect its "transparency" from attack, and then build the wall out of whatever you want. The bigger and more sturdy the better, so there's room on the inside for the massive computers required to make the thing run.

Since you've already got sophisticated computers powering the thing, adding a noise cancellation module seems straightforward.

The Wall is an surreal absurdity.

https://www.nytimes.com/1978/05/07/archives/surreal-and-absurd-surreal.html

The paradox of this kind of literature is that if the symbols are too
easily comprehensible they tend to appear monotonous and‐ trite, while
if they are totally opaque, they offer no purchase for the mind and
merely replace the Absurdist face of the world by an impenetrable
surface of apparently random verbal signs. The ideal solution, not
easy to achieve, is a convincingly pregnant mystery.

With a wall like this, your fiction should be absurdist and surreal. A clear wall separating 2 societies is going to be a metaphor. If you establish that it is clear aluminum oxide that falls under trite. Leaving it up in the air will be frustrating. Best: you can have various characters explain it in detail and have it be different each time. In the absurdist tradition, each citizen can have his or her own persuasion about how the wall works and what it is made of - glass, or wind, or force, or living creatures, or an erotic dream. I can envision the same character who put forth one explanation then putting forth a different one later in the story. If challenged, the character may or may not recall his original explanation, and will good-naturedly try to change the subject.

A dense packing of optical fibres, endlessly rising from the ground. This would give observers the impression of people being inches away that in reality are meters distant. An underground source let's it rise up, taking any damage with it (making it impermeable) and slowly disintegrating in lofty heights (keeping its secret). The height is what makes it unsurpassable. If the world otherwise has never seen a TV-stone no one would figure it https://en.m.wikipedia.org/wiki/Ulexite.

The see- through would be quite limited, but the weird 'right below the surface' vibe of anything that IS seen might make up for it.

You want transparent, AND immune to surface degradation by thousands of years of wind and weather? In a mountain range, thus 100% guaranteed to be an earthquake zone at least in the very long term?
That is a very tall order!

Even a diamond surface would fail the test, you would have to resort to some mumble-fumble-handwaving forcefield or outright magic.

It can't be done in a science-based way.

Diamond might come close, but it's a brittle material. Hit it hard with a sharp point (hardened steel, or rock) and it will crack. Toughened glass is more resistant to cracking, but shatters very spectacularly if you apply enough force (or grind your way through the outer toughened shell). You might try "toughened diamond", with no further explanation. Metals are resistant to cracking, but the physics which makes this so is the same physics that makes them opaque and reflective.

I'm tempted to add that it's obviously a General Products hull derivative, and so Puppeteers must be involved. "One giant molecule with its atomic bonds artificially strengthened using the output of a small nuclear reactor ..." Good handwavium, but impossible given science as we know it.