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First of all, this question is going to seem a a bit of philosophy but know that vague and purposeless wandering is certainly not what i'm trying to propose here.
Also, the reason i didn't post in philosophy communities is that they certainly know a lot less ( if anything ) of quantum mechanics than most of you here.

My question : I heard several times that the results of quantum mechanics (double-slit experiment for instance ) challenge our logic. One example of that is the famous physicist Lawrence Krauss.

He keeps saying that after our discoveries of quantum mechanics, "logic" is becoming flawed.He wears a 2 + 2 = 5 T-Shirt to support his case.

Does anyone know exactly are physics reffering to when they introduce the word "logic" to say it shouldnt be taked for granted ? Would "logic" be common-sense ? would "logic" be sensory experience ? if yes, then i'd highly agree. While we can't experience aurally frequencies out of 20-20khz range we are certain that they do exist.

On the other hand, if "logic" reffers to our deductive and inductive logic then i dont understand.
How could we say that the result of lots of year of deductive and inductive logic ( from Thales to Newton to our modern Science ) points out that deductive and inductive logic is flawed.
Mathematics also rely heavily on deductive logic.Mathematics is also the language in which physics is formally expressed.
Denying or not taking for granted even our "deductive logic" would be not taking for granted Mathematics in which case would end Physics.

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If logic is flawed then er... uh... hmmm... never mind. –  Alfred Centauri Jun 19 '13 at 1:04
    
Seriously though, see "Laws of thought": en.wikipedia.org/wiki/Law_of_thought –  Alfred Centauri Jun 19 '13 at 1:06
    
Inductive logic is a tough cookie regardless of classical, relativistic and quantum mechanics. Just ask the logical empiricists. –  Wouter Jun 19 '13 at 1:49
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The most advanced kind of deductive and inductive logic we have is mathematics. And QM does not violate that. Quite the contrary, QM can be described by mathematics more precisely than any other field of physics. But maybe you mean something else when you say "logic". Maybe you mean intuition, which would be strange since human intuition is often not very logical at all. –  SpiderPig Jun 19 '13 at 2:03
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@nerdy This really would be better suited for philosophy. There certainly is a branch of philosophy of science dealing with QM. What they do, they do rigorously, and it involves discussions such as how much our axiomatizations should include the Law of the Excluded Middle. –  Chris White Jun 19 '13 at 4:01
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closed as not a real question by Chris White, Qmechanic Jun 19 '13 at 12:03

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2 Answers

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On the topic of the actual consequences of QM, here is answers with a few things that cannot be explained without QM.

That aside...

There is a golden rule that one should recite before all theoretical physics studies:

"It all adds up to Normality".
- Greg Egan, Quarantine

The thing with Quantum Mechanics and "logic" is that humans are really bad at QM and really good at "logic".

In fact, "logic" is an actual area of study in psychology: Naïve Physics.

Naive Physics (forgive me not using umlauts) is an all-right approximation of anthropically scaled physical phenomena: Object permanence, an exclusion principle based on volume, absolute time, a primitive notion of gravity...

This is what humans think with, every day, on an instinctive level.

Over the times, you see refinements of Naive Physical concepts in works of Aristotle and Newton.

Object permanence, volume exclusion, gravity, absolute time.

Then relativity comes along and throws absolute time out the window. Believe me, people cried "Logic is meaningless" when relativity was new too.

Then comes Quantum Mechanics: Throw away volume exclusion and even to a degree the intuitive notion of Object Permanence.

There is one other concept of Naive Physics which QM seemingly violates: Looking is a free action. Suddenly you chance things by "looking".

So people do indeed cry out "Logic is broken." But it isn't, because Logic has nothing to do with QM.

Logic, and indeed all of mathematics is about Axioms and Theorems and the steps of inference in between. QM's apparent weirdness has no effect on me using the Peano Axioms to say:

$$ \begin{array}{l l}\vdash & 0 = 0 \\ \vdash& \forall x, y : S(x) = S(y) \iff x = y \\ \vdash& \forall x : x + 0 = 0 + x = x \\ \vdash& \forall x, y : x + S(y) = S(x) + y \\ \vdash& 2 = S(S(0)) \\ \vdash& 5 = S(S(S(S(S(0))))) \\ \vdash& 2 + 2 = 2 + S(S(0)) = S(2) + S(0) = S(S(2)) + 0 = S(S(2)) \\ \vdash& 2 + 2 \not = 5 \\ & \iff S(S(S(S(0)))) \not = S(S(S(S(S(0))))) \\ & \iff S(S(S(0))) \not = S(S(S(S(0)))) \\ & \iff S(S(0)) \not = S(S(S(0))) \\ & \iff S(0) \not = S(S(0)) \\ & \iff 0 \not = S(0) \\ \end{array} $$

Captial L Logic is set in mathematical stone and to say that QM's "mysteries" imply $2 + 2 = 5$ is juvenile, trivially untrue, and shows that the speaker hasn't really understood anything at all. It is like saying:

Boy am I bad at abstracting from my everyday life and interactions, that I cannot even sit down and actually learn QM. I am going to put that on a T-shirt!

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"to say that QM's "mysteries" imply 2+2=5 is juvenile, trivially untrue, and shows that the speaker hasn't really understood anything at all." OR the speaker has more interest in grabbing headlines than educating. Which doesn't sound like anyone famous... ;) –  Michael Brown Jun 19 '13 at 2:09
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The way in which one may have a point when claiming our logic is broken by QM in a mathematical way is the following.

Usually (classically), we think of the state of a system just as an element of some (abstract) collection and we infer equivalences, bijections, unions, cross-sections and we use Boolean logic to determine probabilities (i.e. we assume the system is always in 1 definite state).

In QM, it turns out we need to think of states as being (unit) vectors in some abstract vector space. Vectors in such a space can be written as combinations of a few basis vectors and so the state of a system can be a combination as well. This is superposition and it changes the way we calculate probabilities.

So it's not that logic itself is broken, really. It's just that we use a different kind of logic in QM than what we're used to, you could say.

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