Can a hard fork effectively double the value held in bitcoin? A hard fork necessarily means that two versions of the block-chain exist and value is held in both. Now realistically one of them should probably go down in value and the other increase or hold steady such that the total value held in them is roughly the same at the end of the day ( assuming a rational crypto-currency market). However assume that the market is undervalued and somehow the market decides that both the blockchains have the same value or that the new one is way more valuable than the older one, with the latter holding its value; isnt that equivalent to something like 4 billion dollars of value being created out of thin air? And also, how likely is that scenario, especially in the context of bitcoin classic....
I'm not an economist, but…  

No, that's very unlikely.
Starting from your assumption that the network splits into two persisting blockchains*:


The number of active participants of each network is reduced. This reduces the utility of the network. → Negative effect on the value.
The amount of transactions that can be sent increases. This improves the utility of the network. → Positive effect on the value.
The shortterm security of both chains is reduced as hash power is spread to two chains. → Negative effect on the value.
The longterm security of both networks is reduced, as one or both of them become more likely to cease existing. → Negative effect on the value.
Unforeseeable reactions of various invested parties. → Unknown effects.


Shortterm:
I'm fairly confident that a project fork would throw the community into turmoil. Some developers might leave, some companies may be bankrupted, lots of users would lose money. The community would have to reorganize, work on governance, work out new goals, and rebuild teams. Blocks will slow down due to hash power splitting to two chains. The underdog may use this opportunity to completely redefine themselves, thus bringing their project back into the game. Development would slow down significantly for a while. I would expect each chain to have a lower value than the original chain, most likely the sum of both would fall well below the original chain's value.

Longterm:
I'm convinced that cryptocurrencies benefit so strongly from the network effect, that only a small number of them will be able to coexist, i.e. both blockchains would be competing for the same market share. Either they diversify to an extent where they appeal to vastly different userbases, or balance will at some point tilt, causing one side to take the lion's share. Even if the projects significantly diverge, one should end up much more widespread than the other. Should this schism have a clear victor quick enough, the winner, now improved in comparison to the original blockchain, could attract the bulk of the community, and rally. If they split without a clear majority and the schism drags on, it might become so ugly that both bleed support and go extinct.



*It's not clear that two chains would persist after a hardfork. The game theory seems to work out in a way that one chain would very quickly be abolished.