Is the object uniquely determined when using は in the following sentences?

Question

卵は私が食べた。Speaking of the egg, I ate.

Is what I ate the egg? Is it possible that I ate something other than the egg?

Answer 1

「[玉子]{たまご}は[私]{わたし}が[食]{た}べた。」

If this were the only sentence given, all we know for sure would be that the speaker ate the egg.

The sentence says nothing about whether or not the speaker ate something else besides the egg. Maybe he did and maybe he did not. The speaker just did not mention it.

One could add another sentence using 「も」 as in:

「ハムも私が食べた。」

to say one ate the ham as well.

Finally, if a John ate the bread, one could add the sentence:

「でも、パンはジョンが食べた。」

or

「でも、パンを食べたのはジョンだ（or だった）。」

Answer 2

Everything l'électeur said was correct. Given this, it's certain that the speaker ate the (or "an") egg.

There's a little more to this, though. Real statements don't usually exist in a vacuum; they exist in some context. In this case, some of the context is actually built into the sentence.

卵は私が食べた As for the eggs, I am the one who ate them.

(I translated 卵 as plural to tie in with the following interpretation...)

This sentence structure strongly implies that it's answering a question like "who ate the bacon and eggs?"

Aさん：　誰がベーコンと卵食べた？　Who ate the bacon and eggs?
Bさん：　卵は私が食べた。でも、ベーコンはジョンがたべた。　I ate the eggs. But, John ate the bacon.

卵は and 私が really give off the feeling that you're contrasting with another sentence. If you don't want to give this feeling, then you might use this:

私は卵をたべた。As for me, I ate the egg.

However, as you can see in the English "As for me", this really stresses the fact that the speaker did it. This again implies contrast; the speaker wasn't talking about his or her self before this, or else is being emphatic.

You can avoid this by going to the simplest, least emphatic form:

卵をたべた。 I ate the egg.

In the context of a real conversation, where both parties know who they are talking about, this is unmistakably "I ate the egg". Someone who just walks in when the speaker is saying this would have no idea who ate the egg in question, but that person isn't the intended audience anyway! It's certainly no less vague than "he ate the egg", which can refer to one of the roughly 3.5 billion males on the planet.