Well this is a pickle but perhaps by answering a few more questions the path may become more clear.
First have you ever been in another relationship before? If so then ask yourself if you were physically satisified in that relationship. What was different about it that seemed to make you happier with it? If you were not satisfied in that relationship then I'd be willing to suggest that perhaps the problem is not with the women but with some need you have that has yet to be discovered. If that's the case then I say talk to your girlfriend ASAP because you two have some work to do to find what is missing.
Second, ask yourself how important this physical satisifaction is when compared to the intellectual and personal aspects of the relationship. Every person holds these aspects with different weights, and it may be that you value the intellectual or personal relationship more than you give credit for at the moment.
If it turns out the passion is important to you then you need to have a talk with the current girl. You need to explain your problem and one of two things will happen: she'll decide to experiment with things to find out why the passion isn't there or she'll decide to bail. This is technically a win-win situation, as I will explain.
People treat relationships (whether they admit it or not) much like business deals. There are sacrifices made to maintain the relationship and in return benefits come from the relationship. Each person has some cost/benefit function they subconsciously use to determine whether the relationship is worth maintaining or not. As proof I submit the girl you love but do not pursue due to incompatibilities. Perhaps without realizing it, you compared the benefits of companionship with this woman to the costs of dealing with her personality and decided that the costs outweight the benefits.
Communication is very important in relationships, as is honesty. You must tell your current girlfriend the situation as soon as possible. This gives her the ability to reconsider her evaluation of your relationship and decide if she would like to try harder to satisfy the needs you feel are not being provided. If she decides this is not desirable, then she is as incompatible with you as the girl whose personality is not desirable, since she will not satisfy all of the requirements of the relationship. If all of your requirements are not met, eventually the relationship will fail.
I would not suggest a harsh breakup with the current girlfriend, as it seems like the two of you could (to use a cliche) just be friends with no problems. It could be that the appropriate relationship between you two is that of friendship, not matrimony. Six months is honestly a pretty short-term relationship so don't feel trapped or obligated to perform a role you are not obligated to perform.
My explanation may sound harsh and unfeeling but honestly I feel like most unhappy couples today start out this way: either one or both partners feel like the other is "close enough" or that they can "adjust for this one thing". Some things you can adjust for or get used to, but if anything in a relationship is causing you enough turmoil to be unsure whether you should maintain the relationship it is time to talk with the other member immediately. If a breakup occurs, consider that dropping the "boyfriend/girlfriend" roles from the relationship will alter what you expect out of the relationship and probably remove the problems.
Finally, don't look at my suggestion as some kind of sexist "She needs to put out or get out" statement. The "change or leave" sentiment is definitely there, but its basis is on relationship theory rather than any expectations of favors by any party. My suggestions would be the same if you were a woman asking advice about men, or if you were upset because she was an excellent sexual partner but had a personality you despised. As others have said, sex is not everything in a relationship, but if you find you get to the point that you cannot be happy unless she performs acts she is unwilling to perform you will both benefit from a separation. If you are not getting what you want out of a relationship you have to communicate the need to the other individual. If they are not willing to satisfy the need then the relationship must be modified such that the need is no longer there. In your case, if it turns out to be some kind of physical act she is unwilling to do, I feel like the most mature and least damaging thing to do is modify your relationship such that passion is no longer expected (i.e. become "friends" instead of "boyfriend/girlfriend"😉. Removing this expectation will most likely solve the problem.
In summary:
- Talk to her honestly about this subject. You both need to agree whether this is a problem or not. If you think this will turn out messy now, perform a utilitarian comparison between a messy breakup and a divorce and I think you'll agree it's better to stop now than later.
- Figure out why you don't feel passion; if it's something she is or is not doing, talk to her honestly about this subject. If she does not wish to do what you need it is better for you two to redefine your relationship.
- Talk to her about this problem immediately. Triple redundancy really doesn't place enough emphasis on this suggestion. Every single fight I have had with my fiancee has been over a misunderstanding of expectations and a lack of communication of the misunderstanding.
*edit* I decided to add this in because I've been one-sided: when you do talk with her, make sure to ask if she is feeling unsatisfied in any way as well. If she is unsatisfied and you have no issues with making the changes she has requested, by all means you should make an effort to make said changes. Remember, she is performing cost/benefit on you just as you are evaluating her. It is not impossible that you feel no passion because she puts no feeling into her acts because she feels you are not providing something else she needs. This can only be discovered through honest, non-confrontational conversation.
Establish a ground rule before discussion: If, at any point during honest conversation, either of you begins to get angry, terminate the discussion until a later time. When you are angry you act irrationally and can do irreversible damage by saying things best left unsaid. If either of you begins a contest of "well what about the time you did..." you need to stop the discussion and start it again another day. Act not in anger. Ever. I have failed to learn this lesson many times.
Now I have to go and correct a pot -> kettle -> black issue in my life, thank you good sir.
*off-topic edit* Ahahah epic post widens the table I've got to start losing weight!