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This is a major reason why the practice of welding, and soldering, is so complicated.

A lot of what makes welding and soldering complicated is the need to remove, or avoid creation of, the oxide layers that inevitably form on the surfaces of metals. More so, these oxides form faster at higher temperatures. That's why solder wire and stick welding electrodes have flux cores or coatings, why MIG/TIG welding uses a shielding gas, and so on.

I highly recommend everyone take a Welding 101 and 102 class at their local community college. While my primary trade is IT, I'm certified to weld, and I personally think its a lot of fun. It's about not only knowledge, but skill and experience.

You'll be satisfied when you're able to successfully move the "puddle" of molten metal down your weld line, the weld looks beautiful, and then you find out your weld is extremely strong when its destructively tested.

I was going to say this too! I own a TIG and a MIG- welding is alot of fun and the science behind it is interesting.

A perfect combination of science and dexterity.

Need projects? Make furniture or buy an old car! Rust repair without "bondo" is an art!

I've been wanting to do this. How expensive is the equipment to keep and maintain?
Used welders in good condition can be had for under $1000. Depends on if its a MIG, TIG, or "stick" (flux). Traditional welding relies on the shielding gas being generated from a solid material (flux) wrapped around the consumable electrode. Other methods (MIG and TIG) rely on inert gasses being provided by separate support equipment to a "gun", which is also feeding electrode wire.

To take the class should only cost you book and tuition fees. My total out of pocket at a community college in the Chicago suburbs was ~$600 for three classes (Welding 101, 102, 110).

EDIT: I have a whole box of welding books. If you're serious, I'm more than happy to ship them to you.

Which suburb? My wife Erin took welding at Triton in Tyne near west suburbs and liked it, but they shut the program down before she could take the advanced class.
My classes were at Elgin Community College (I was living in Saint Charles at the time). Unfortunately, its quite the haul from Chicago.
One note: if you have a MIG welding rig you can use flux cored wire in it without a shielding gas, which simplifies things somewhat if you're an occasional welder. Just make sure to adjust the polarity settings correctly when you do (there are tons of videos on youtube explaining how and why).
You're just not pushing hard enough.

https://en.wikipedia.org/wiki/Explosive_welding

As I understand it's not bonding chemically.

"The process does not melt either metal, instead it plasticizes the surfaces of both metals, causing them to come into intimate contact sufficient to create a weld. "

You don't need to melt the metal for there to be "chemical bonding". And now for me to probably mangle what I remember from material science.

When you're dealing with metals (and alloys) you're pretty much dealing with a lattice of atoms. It's not very useful to talk about individual atoms "chemically bonding" with each other, or at least not the way you would talk about say... bounding sodium and chlorine to get table salt, or nitrogen with oxygens to get nitrates.

Instead, you have this lattice of metal atoms, within which you can incorporate other atoms. Say you had a lattice of iron. By incorporating other metals into the lattice (say magnesium, or nickle), or even other non-metallic elements (most famously carbon) into the lattice, then you get different alloys. But at no time are you actually bonding say an iron atom with a carbon atom making a "steel molecule".

So when you weld dissimilar metals/alloys, what you're trying to do is to get two dissimilar lattices to "blend" into each other. When you have a crappy weld, one of the things that happen is you get a crappy boundary layer (potentially of stuff like metal oxides) sitting between the two lattices. Whereas if you have a "perfect" weld, the two lattices will seamlessly merge into each other - you'll get this diffusion zone. In the case of two similar metals, then the two lattices can actually perfectly merge - that is what Feynman is trying to get at there.

So, back to the point. Creating a good weld is in many ways as close to "chemically bonding" as you can get with metals / lattice structured materials. Or at least, in a useful sense.

Correct me if I'm wrong but isn't this why panning for gold in rivers was so prevalent through history? Flecks of gold would naturally cold weld over a millennium of being knocked around in the water.
I can't speak for all of history but at least in the US West gold panning was used to locate rich ore veins upstream. The idea is that you pan for gold, steadily moving up the stream until the relative amount of gold flakes drops, meaning you've gone just a bit too far and you probably now have a great idea of where a lot of gold is.
This was the primary source of 'stiction' in the disk drive business. Platters became optically smooth, read write heads similarly. When the heads "landed" on a spot where the lubricant had migrated away from they would bind so tightly the motor couldn't break them free. (old SparcStation drives you could take them out. give them a sharp twist along the platter's rotational access, and if you were lucky move the heads to a space they wouldn't bind to.)
Many summers years ago, during an internship, I got tasked with setting up a development machine from old parts lying around the office. One of those parts was an, even at the time, ancient hard drive. When I first powered the computer up everything turned on just fine, but it couldn't recognize the disk. I'd run into bad hard drives before, no big deal.I went to my bosses boss, an older engineer who had seen a thing or two, and told him we'd need another drive. He took the thing out and gave it a good hard twist, and told me to try again. Lo and behold, it worked!

He explained that sometimes when older hard drives have been powered off for many years the head some times sticks to the platter and doing what he did can fix it. I could barely believe that the phenomenon was actually real. I've spoken to a few people over the years about heads sticking to platters and it turns out, while it isn't (or wasn't?) exactly common, it's not exactly rare either.

Is this not an obvious answer? I am genuinely curious why the impurities and oxidation are not the answer the OP jumped to.
When you know you have basic but not expert knowledge you can make an educated guess (or several), but in the absence of empirical evidence you acknowledge there could be other factors you haven't thought of.
The hatches and frames on the Mercury and Gemini capsules had to be well painted because the exposure to vacuum raised the danger of like metals welding together.