FrediFizzx wrote:This seems a bit abstract. I suppose h is an index for hidden variable? I think you explained the inequalities better when describing the indices that are usually missing.
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minkwe wrote:On these forums, we have spent many years arguing about inequalities. But do we really understand what they mean? I'm becoming convinced that often, inequalities are easy to misinterpret because they are by definition incomplete mathematical expressions. For example the expression
can be written in incomplete form as
But this obscures the claim about
Heinera wrote:I guess you meant to write .
But I anyway don't see why must contain any extra information here.
minkwe wrote:On these forums, we have spent many years arguing about inequalities. But do we really understand what they mean? I'm becoming convinced that often, inequalities are easy to misinterpret because they are by definition incomplete mathematical expressions. For example the expression
can be written in incomplete form as
But this obscures the claim about
Some times, the terms needed to understand the meaning of the inequality are precisely the ones that have been hidden/removed. So in this thread, I'm hoping we would carry out a simple exercise with Bell's inequality. For Bell's theorem, using the wikipedia form:
In other words using my earlier symbols:
What is ?
Let us complete the expression with the full form of z. Let us do the derivation of the equality rather than the inequality. Once we are done, let us examine what it means to say .
FrediFizzx wrote:minkwe wrote:On these forums, we have spent many years arguing about inequalities. But do we really understand what they mean? I'm becoming convinced that often, inequalities are easy to misinterpret because they are by definition incomplete mathematical expressions. For example the expression
can be written in incomplete form as
But this obscures the claim about
Some times, the terms needed to understand the meaning of the inequality are precisely the ones that have been hidden/removed. So in this thread, I'm hoping we would carry out a simple exercise with Bell's inequality. For Bell's theorem, using the wikipedia form:
In other words using my earlier symbols:
What is ?
Let us complete the expression with the full form of z. Let us do the derivation of the equality rather than the inequality. Once we are done, let us examine what it means to say .
So . Now what?
.
minkwe wrote:On these forums, we have spent many years arguing about inequalities. But do we really understand what they mean? I'm becoming convinced that often, inequalities are easy to misinterpret because they are by definition incomplete mathematical expressions. For example the expression
can be written in incomplete form as
But this obscures the claim about
gill1109 wrote:minkwe wrote:On these forums, we have spent many years arguing about inequalities. But do we really understand what they mean? I'm becoming convinced that often, inequalities are easy to misinterpret because they are by definition incomplete mathematical expressions. For example the expression
can be written in incomplete form as
But this obscures the claim about
I was taught that is *defined* to mean that .
So what you call "an incomplete form" is not *incomplete* at all. Of course, it can be useful to know how the various symbols you are using were originally defined.
Usually, we don't just introduce new symbols but we also prove useful properties of them, so that we expand not just the collection of words in our language but also establish new ways to derive true statements in the language from already established true statements.
For instance it is a *theorem* that if and then
minkwe wrote:Any objections to this analysis?
Heinera wrote:8' is correct. But it's also pretty uninteresting, since it can't be tested empirically, not even in a thought experiment. Nor does it have any QM counterpart that you could compare with. The only definite thing you can theoretically conclude about the RHS in 8' is that it can never exceed 2.
minkwe wrote:Experimentally, as N>>1, 8' becomes:
Heinera wrote:minkwe wrote:Experimentally, as N>>1, 8' becomes:
This makes no sense. Your LHS is not . And the RHS has nothing to do with .
What is ? Is it supposed to be ?
Heinera wrote:For one thing, why are there no function B(...) on LHS? Have you completely forgotten about Bob?
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