subject verb inversion - Omitting whether (if): Not sure if we can do this

I'm not sure if(or, whether) we can do it.

Can this sentence be written in this way...

I'm not sure can we do it.

Can whether, or if, be omitted like that and still be understandable?

Thanks.

Answer

Consider first this question on omitting "that" from a sentence. As the answer says, we can omit it when it is used as a subordinating conjugation, though there are some cases where it remains either necessary or clearer (this article has more advice on that).

Now, having considered that, consider that when we change from:

She told me that it was okay.

To:

She told me it was okay.

In the result we don't really have an omitted that. What we have is an independent and a dependent clause conjoined together by nothing. Granted in this case that is the only English word that could do the job, but that doesn't really make any difference; if English had a million such words, or if someone's idiolect meant they often used que there, the result would be the same.

So really the phenomenon isn't that we can omit "that" at all, but that we can omit subordinating conjunctions.

In the examples you give here, if and whether are being used as subordinating conjunctions. And so they can be omitted similarly:

I'm not sure we can do it.

Now, we can't say looking at that whether it was if, whether or that which was omitted, again because it wasn't really any of them; we have subordinating conjunction happening without a word doing the task. The meaning is the same either way (and if not, that's a clear sign that you don't have a case where the omission is safe). Dropping if and whether here follows the same restrictions as mentioned in the two links above for that.

Inversion does something completely different:

We can do it. — Indicative statement.

Can we do it? — Question formed by inverting the modal verb in the indicative.

This doesn't mix in with the omission of if or whether because it doesn't work without the omission:

*I don't know if can we do it?

You could combine the two clauses with a comma or full stop, but then it's something different again:

I don't know. Can we do it?

This is not an omission of the subordinating conjunction; it is making the two clauses more fully separate so while it arrives at something grammatical, the meaning is completely different.