If, during the split, neither side makes any changes to the protocol which would invalidate blocks from the other side, then whenever the two chains were reconnected the chain with the most proof of work (note - not necessarily the longest chain) would be the winner. All the nodes on the losing chain would switch over to the winning chain, and all the blocks the losing chain had mined during the split would be invalidated.

If one of the sides did make any changes which would prevent this from happening, then there would indeed be two blockchains going forward, and everyone would end up with the same number of coins they originally had on the other chain at the time of the split.

I agree. In the highly unlikely scenario that there would be two separate internets for even a period of a few months, then I suspect one or both chains may deliberately create a fork which would keep the two chains separate in the event that the barrier between them was removed.

Because of difficulty changes.

Let's say the internet does split in to two. After a couple of readjustment periods, the difficulty on both chains will have readjusted to the decrease in hash rate, since a proportion of the hash rate has just disappeared from each chain and is mining a different chain. Let's say Chain A is left with 70% of the global hash rate, and Chain B is left with 30% of the global hash rate. The difficulty on Chain A will adjust to around 70% of what it was, while the difficulty on Chain B will adjust to around 30% of what it was. Both chains will continue to mine blocks every 10 minutes on average, but these blocks are not equal in terms of the amount of work done. It requires significantly more work on Chain A to find a valid block than it does on Chain B.

There will of course be random variance between the two chains, so they will not find blocks at exactly the same rate, and as we know, hash rate can come and go which also affects the rate of block creation. If these two chains were to merge and Chain B happened to be longer, it would not necessarily have more proof of work since it has done less work overall than Chain A has, even with more blocks, since these blocks were much easier to find.

The primary problems that reconciling the split cause are the invalidation of block rewards and the possibility of double spending.

• Block rewards in the shorter chain would be invalidated. That could create a huge problem if the split is longer than 100 blocks and the miners spend their block rewards.
• If a UTXO is spent on both chains but differently, then one of the transactions (and all of its subsequent UTXOs) will become invalid when the chains are reconciled.

For that reason, I believe that the users of one or both of the chains would probably do a hard fork in order to avoid this situation.

In a reorg, the unique transactions in the shorter chain are returned to the mempool and re-confirmed in subsequent blocks.

A sudden segregation of WWW will result in the blockchains being split with the connections to external addresses being restricted and the chain being able to continue within its own bubble only. If a state is willing to do this, they can easily either ban Bitcoin completely or basically negate any benefits Bitcoin provide, due to the effective sybil being done on the citizens.

Whether they will piggyback on Bitcoin or make their own remains to be seen. Without completely removing encryption, Bitcoin can still function within the bubble itself but it won't be able to transmit any information outside of it, provided that there isn't any efficient system to maintain consensus with the other systems.

If something like that happened, Russia + China would ban Bitcoin and everything related to it, and Bitcoin on this network would either be abandoned or forked to be more like Monero - more private and mined on home computers, because big mining farms would be impossible under ban.

Theoretically, it could be possible to make an algorithm to merge both chains into a new one, minus the inputs that were spent on both chains (but if this percentage is huge, that would be a big problem). But I doubt that existing holders would be happy about it, so such fork would most likely be doomed to fail.

Keep in mind that this "split" you are talking about would require the internet to be split in such a way that leaks don't happen.  If even 1 person somewhere in the world can find a way to run 2 nodes (one on each network) and then connect those two nodes together (even with a physical wire he runs himself) then the blocks and transactions will make it back and forth between the two networks, and there will not be a chain split.

It wouldn't even be necessary to get unconfirmed transactions to leak between the split networks.  As long as the blocks could be transferred, Bitcoin could remain unsplit.

So, it would even be possible for something like 2 ham-radio operators to coordinate to transmit the blocks from one side of the split to the other.

It wouldn't be possible.

Let's say that I, a person on Chain A, want to send coins to you, a person on Chain B. I already know one of your receiving addresses from previous interactions with you, so I create a transaction sending one bitcoin to that address and broadcast it to my local nodes, which are all obviously on Chain A. My transaction propagates through Chain A, is picked up by miners on Chain A, and is mined on Chain A. On Chain A, you receive 1 BTC.

However, since the two chains are completely split, the transaction is never broadcast to Chain B, and the block my transaction is confirmed in is not valid on Chain B, not that Chain B would be aware of it anyway. On Chain B, which is the chain you are running on, you have received nothing, so there is nothing to sell.

If my transaction did make it through to Chain B, then the chains aren't separate, and so everyone's transactions could make it through to Chain B and vice versa, meaning there wouldn't be a chain split. As DannyHamilton has pointed out above, even the smallest leak relaying blocks back and forth would prevent a chain split.

Okay got it. How about this

Suppose I am on chain A and then pay someone to get some amount of work done.
Then I travel to the other side of the internet. I get to access all my funds on chain B and then pay someone to do more work and pay him through the funds on chain B.
So this way I get double the work done while spending half amount indirectly.
Yes, it exactly works like a fork.  

[Feels Overwhelmed - Feels like two lives]

This is real possibility and Russia has been preparing for this internet split scenario with moving lot of servers in their country, they already have their own social networks and search engine,
same thing applies for China that is gone few steps ahead in that direction, and they are even spreading their CBDC coin that may be the reason they did coordinated ban on Bitcoin.
If each country have their own separate Bitcoin chains that would mean that all other financial systems will be separate, without credit cards, paypal and other services working globally.

As we are talking about internet shutdown, that should also not be excluded at least temporary for few days or weeks, especially FEMA released this news for nationwide emergency alert scheduled for August 11th
with messages sent to all TVs and Radios, including cell phones that opted-in to receive them:
https://www.fema.gov/press-release/20210611/fema-and-fcc-plan-nationwide-emergency-alert-test-aug-11-test-messages-will