There's such fierce debate on this thread that I thought long and hard before posting... But I thought rather than trying to convince anyone whats wrong or right I would simply share my own personal experience.
I've tried to read most of the posts on this thread so i'm up to speed but forgive me if I've missed anything.
Firstly in order to answer the original question, "can you be long and short at the same time?"... from my understanding the answer is: that depends on your broker and I think its primarily a case of whether you're based in the US or not.
With a UK broker for example, if you really wanted to go long and short the same currency pair then technically you can.
That leads on to the other issue which is whether or not there's any benefit that can be derived from being positioned this way. I fully agree that its a zero sum game and in fact your doubling your trading costs when you can in-fact just be flat.
But in my particular example I have to be able to be long and short at the same time because I have several different strategies that my system employs. These strategies were created independantly of each other and often have different hold times. For example, I am often Long GBP/USD one strategy (10 days hold) and short GBP/USD on a different strategy that has a 7 day hold.
But even then its not necessarily a case of different hold times. I can have two different strategies that have the same optimum hold time on a given currency and they can also generate long and short signals at the same time. When they do this I still have to execute each set of trades because my statistics have been calculated on the premise that you trade every single signal.
So if strategy A has win rate of 70% and so does Strategy B I just have to accept that when they're both on, one is going to be a winner and one is going to be a loser. But this is fine, in this circumstance the benefit of doing this is not a monetary one, the benefit is that I can carry out the key task of trading each individual strategy how it needs to be traded, and this ensures that my returns are inline with the analysis that was carried out under the assumption that every signal is traded. For me trades are generated every hour and positions are built up over time so its not really even feasible to just say I'll go flat when I get long and short signals.
Finally, even if you were to consider the very same strategy, on the same currency, exact same hold time, and the system went long and short at the same time this still doesn't necessarily have to be a zero-sum game.
If a strategy has the following setup
SL: -100 pips
TP: +300 pips
If you went long and short at the same time and price moved over 300pips UP then you would actually make a net profit of 200 pips. This is because the short would have stopped out -100pips and the long would have taken profit at 300pips. Of course there is also a chance that both your stop losses could be triggered if price reverses before hitting the take profit, in this case you'd actually end up being down -200pips.
So in my humble opinion, if you're trading the same trade size that all goes on at once, holding it for the same amount of time, without stop-losses or take-profits then it truly is a zero-sum game. But like I hope I've illustrated above there can be several reasons why you may have to be long and short at the same time and it could be beneficial, whether in a non-financial way, like ensuring you trade your system/strategies how they need to be traded, or for financial gain because they have different hold times etc and going neutral or one way or the other isn't necessarily a practical option.