Critique of the Social Contract

What justifies the state? For some philosophers it is the “social contract”, or contract theory. But what is a contract? Is it not an agreement? But what is to say that the contract is binding? It would seem that the contract requires something external to it self to give it meaning. Indeed the very notion of “justifying the state” indicates that there is a principal of justice external to the state to which it must answer. It would then seem to be the nature of this external principal that should be the focus of our study if we are to truly justify the state.
Unfortunately, Thomas Hobbes did not seem to grasp this. He supposed that we all start out as a bunch of troglodytes hitting each other (free for all) over the head with clubs, until some of the troglodytes get together and form a state by agreeing to accept its authority. But what validates this agreement? It cannot be the state, for the agreement must be valid in order for the state (or any principle there of) to be formed. So for the state to validate the agreement it would have to be and not be in the same time and in the same relationship, which is a rational absurdity.
John Locke proposed a means around this problem with the concept of natural moral laws. These laws being external to the state can thus be used to determine if the state is legitimate. The state is then just if it upholds and adheres to the natural law, and unjust if it does otherwise. So far so good. But then Locke had to go and drag democracy into the matter. You see according to Locke it is the majority that ratifies the interpretation of natural law. But this is leading us right back to the problem with Hobbes. If the majority is a product of the state, how can it validate that which is prior to the state? Or another way of looking at it could be through physical law. The speed of light is 300,000km/s if 99.999% of the population said it was 25km/h it would not change the speed of light 1m/s (although I suppose you could say it would etymologically change the meaning of kilometer and hours).
Jean Jacques Rousseau had a somewhat different approach. To him “man is born free, but everywhere he is in chains”. How can this be? In a rather interesting philosophical maneuver Rousseau proposed that man actually freely submitted to the chains to increase his freedom. This is done through a sort of collective enterprise. Take a man living alone on a desert island. He may be totally free in a certain sense, that is he does not have to trouble about other humans. But he is not free to travel to the moon, or go to a ballet. For these he must surrender some of his freedom to a collective that then will have the freedom each individual lacks. Rousseau viewed society as operating under a similar principle. The individual gives up some freedom so that the whole can enjoy a greater overall freedom. Still it is relying on something external to itself to make it valid. It presumes that the freedom of the individual is theirs to give to the collective for its greater overall freedom. This may be but it is not demonstrated by the theory itself.
In the end all contract theories have the same problems, they assume contracts should be kept and that man has the initial moral capital to enter such contracts. Neither proposition is proved by the contract itself and thus requires something else to do so. It would then be that something else that would then be ultimate grounds of legitimacy for the state.