This iffy whether

David Sax does not like the idea of restaurants charging a gratuity fee. After all, “Once that tip is locked in, who cares if the fish is cold” ("Hey, Waiter, How Much Extra Do You Really Expect?"/NYT). Actually, if (or in case, under the condition that) the fish is cold, David Sax has every right to send it back to the kitchen. What the gratuity fee generates, however, is that the personnel may stop caring whether the fish is served steaming hot or lukewarm.
If introduces a condition, a chance that something might happen while whether announces an alternative. For Luis Tavarez, the parent of sixth- and eighth-graders at Creighton it, therefore, doesn’t “matter if my children are learning" ("Arizona Grades Teachers on Fluency"/WSJ). What matters to him, one might hope, is whether they learn something in school.
It might also matter to him how much his children follow every trend, and he may ask them whether they would also follow “if everyone else jumped off a cliff.” Another, similarly trite question is “if the old rule, ‘Men and women can’t be friends’ still remains true” (“Friendships without benefits”/The Daily Aztec). This question requires whether instead of if since it suggests the alternative of this rule being true or false.
A complete mess was created by Donald Rumsfeld (not only) when he declared that “The Federal Government should be the last resort, not the first. Ask if a potential program is truly a federal responsibility or whether it can better be handled privately, by voluntary organizations, or by local or state governments.” Since he addresses the alternative of programs being federal, state, or private responsibilities, he should have encouraged his audience to “ask whether a potential program is truly a federal responsibility or can better be handled by local or state governments, or privately by voluntary organizations.”
Whether the answer would be in favor of government or private organizations, it should be honest because “Lying to a federal investigator is illegal under oath or not” (”Who’s Not Sorry Now?”/NYT), although this sentence should have included the word whether before the alternative “under oath or not.”
The puzzle whether to use if or whether can be solved by asking whether it is possible to replace if with “in case.” Then if is correct. When, however, an alternative is suggested, whether is correct. Hence, the Vicomte’s exclamation “God help us whether or no!” (S. Weyman, The Abbess of Vlaye ) is indeed "senile," while Charles Dickens' wondering “whether she was engaged, whether she was pretty, whether she wore much bustle, and many other whethers of equal importance” ("Sentiment") is deft.