Talk:Consistent histories

Please, more complicated!
I know, it's about QM, but take a look at the page about the Copenhagen_interpretation. This article can actually be read and understood by a non-physicist. This here is a page from a QM book, not an article in an enceclopedy (isn't that what Wikipedia should be?)

Please, less complete and harder to understand!
The article should be understandable without reading the referenced articles. But it is not the case: JPB (talk) 15:07, 28 August 2015 (UTC)
 * Could someone add a definition for $$\hat{P}_{i,j}$$? Telling that it is related to the proposition $$P_{i,j}$$ does not unambiguously define what the operator is; if fact it does not define it at all. I simply don't want to buy an article or a book to know what it is and then come back here to go on reading this article. The article has to define what it is talking about. If it's too difficult or not the place to define a mathematical item, then just remove the mathematics.
 * What means $$\hat{P}_{i,j}(t_{i,j})$$ ? I guess that $$\hat{P}_{i,j}$$ is not a function of time t, so that anything such as $$\hat{P}_{i,j}(t)$$ would be inconsistent.
 * If I am wrong and if it is consistent, then could someone tell me in the talk page what would be $$\hat{P}_{i,j}(t_{i,j} + 1\;year)$$ so that I can figure out what is $$\hat{P}_{i,j}$$ as a function of time?
 * For me, the most important thing with mathematics is to be able to understand the nature (or quality, or qualification, as you may prefer) of each mathematical object because only then I can try to evaluate what means a mathematical statement. If the nature of the object is not clear, then it is simply not mathematics.


 * And if $$\hat{P}_{i,j}$$ were a function of time, why the time parameter appears only once in the left hand of the formula and not in the development in the right hand of the formula?
 * $$\hat{C}_{H_i} := T \prod_{j=1}^{n_i} \hat{P}_{i,j}(t_{i,j}) = \hat{P}_{i,1}\hat{P}_{i,2}\cdots \hat{P}_{i,n_i}$$
 * This is in the "Consistency" paragraph, so be consistent!
 * The fact that an operator is [to be] defined relatively to a proposition that is related to the time it make sense to be evaluated, does not make the operator a function of time!


 * It is said that the "past" operators with smaller values of $$t$$ appear on the right side, and the "future" operators with greater values of $$t$$ appear on the left side but exactly the opposite is written in the formula. Indeed, $$\hat{P}_{i,1}$$ is related to the proposition $${P}_{i,1}$$ which is evaluated at time $$t_{i,1}$$ which is the smallest of all time values, hence it is a "past" operator and, as stated, should appear on the right side, but in the formula it appears on the left side. The formula should be corrected as:
 * $$\hat{C}_{H_i} := \cdots = \hat{P}_{i,n_i}\cdots \hat{P}_{i,2}\hat{P}_{i,1}$$

Incoherent use of logical OR?
I find the use of OR confusing in this article. Ordinarily a state of affairs that satisfies a AND b also satisfies a OR b. But this article begins by suggesting that a OR b excludes a AND b. (It asserts that a OR b is an example of an inhomogeneous history even though a OR b does not usually exclude a AND b, and so under the usual interpretation, a OR b could still be a homogeneous history.)

That's fine — in that case, OR is just a synonym for XOR, and that might even make sense since the premise seems to be that a and b are not mutually consistent, and so the probability of a AND b is zero.

But then later, the article calculates the probability of a OR b as the sum of the probability of a and the probability of b minus the probability of a AND b! That's consistent with the usual definition of OR. But either the probability of a AND b is always zero, in which case it is unnecessary to mention here, or it may be nonzero, in which case the beginning of the article defines OR as XOR, but this later part defines it as OR. The article seems incoherent either way. 100.11.144.52 (talk) 05:43, 24 January 2018 (UTC)

Incoherent use of logical OR, again
Since no one addressed the other editor's comment from four years ago, I'll post as well. How is it that $$H_i \lor H_j$$ is necessarily incoherent if $$H_i$$ and $$H_j$$ are coherent ("Histories" section)? What if $$i = j$$? What if $$H_i$$ and $$H_j$$ are "adjacent subhistories" (my term) of some coherent history $$H_x$$? This needs clarification. Frankly, the whole article could stand to be looked at by someone who better understands the subject. BrianH123 (talk) 13:40, 23 August 2022 (UTC)