"Beyond a reasonable doubt" refers to the requirement for the prosecution to PROVE exactly how, why, and when the alleged crime took place, by the alleged criminal. There are elements of each crime, which the prosecution must prove, BARD. If all are not present, i.e. one or more are mere supposition, coincidence, or unprovable, then a jury is supposed to acquit. That is their job. That is why a jury that convicts in such circumstances is dangerous.
Remember, our system is supposed to give the defendant the benefit of the doubt. Not to be confused with us "civilians" out here. We're free to say kill the sucker, he's gotta be guilty. Those folks entering deliberation in the jury room must be held to a higher standard.
No, I do not have it backward. Your terminology is incorrect. The key word is REASONABLE. Not just doubt. The standard is not "beyond a reasonable doubt." The prosecutor must "prove to the exclusion of reasonable doubt" that the accused did the crime. They do not have to prove how, when and why. Under your standard, we could all go out and kill with impunity. You would reward a criminal who has the ability to cover up a crime. The jury who are given detailed instructions stating that they can only find REASONABLE doubt if they can explain the evidence within the REASONABLE scenario that is giving them doubt. Otherwise, according to your standard, someone could say, "well, it must have been those little green creatures I see at night. They took her." Some juror may have a doubt but if it is not REASONABLE considering the evidence presented, they must convict. Why do you assume I'm not a lawyer??
REASONABLE DOUBT - The level of certainty a juror must have to find a defendant guilty of a crime. A real doubt, based upon reason and common sense after careful and impartial consideration of all the evidence, or lack of evidence, in a case.
Proof beyond a reasonable doubt, therefore, is proof of such a convincing character that you would be willing to rely and act upon it without hesitation in the most important of your own affairs. However, it does not mean an absolute certainty.
The notion of "reasonable doubt" means that there is no plausible alternative scenario which would explain the facts. For example, suppose that someone were accused of robbing a convenience store and the only reasons the police fingered the suspect are (1) he was found within a few blocks of the store, and (2) he resembled the person on the security video. In such a case, the defendant could suggest to the jury that the store was robbed by someone who looked somewhat like the defendant (but wasn't him), and that the defendant was in the neighborhood for some other reason.
In the Scott Peterson case, there are many aspects of Scott Peterson's behavior for which no plausible explanation comes to mind other than him having either killed his wife or otherwise been involved with her death. Although there might have been some plausible scenarios where Scott Peterson's involvement would not constitute murder, it would have been up to Mr. Peterson and his attorney to suggest one. As far as I know, they have not.
I would add in closing, by the way, that if a person has involvement with another's death that falls short of murder, but works to conceal or destroy evidence showing the specifics of such involvement, it is the fault of that person, rather than the state, if he is convicted of murder.
You don't even need a body, FGS.