Reconciling Schrödinger's Cat with the Principle of Explosion

@browser32,

You asked, does QM follow classical logic ? No.

Quote:

In quantum mechanics, quantum logic is a set of rules for reasoning about propositions that takes the principles of quantum theory into account. This research area and its name originated in a 1936 paper[1] by Garrett Birkhoff and John von Neumann, who were attempting to reconcile the apparent inconsistency of classical logic with the facts concerning the measurement of complementary variables in quantum mechanics, such as position and momentum.

Quote:

Differences with classical logic
Quantum logic has some properties that clearly distinguish it from classical logic, most notably, the failure of the distributive law of propositional logic:

p and (q or r) = (p and q) or (p and r),
where the symbols p, q and r are propositional variables. To illustrate why the distributive law fails, consider a particle moving on a line and let

p = "the particle has momentum in the interval [0, +1/6]"
q = "the particle is in the interval [−1, 1]"
r = "the particle is in the interval [1, 3]"
(using some system of units where the reduced Planck's constant is 1) then we might observe that:

p and (q or r) = true
in other words, that the particle's momentum is between 0 and +1/6, and its position is between −1 and +3. On the other hand, the propositions "p and q" and "p and r" are both false, since they assert tighter restrictions on simultaneous values of position and momentum than is allowed by the uncertainty principle (they each have uncertainty 1/3, which is less than the allowed minimum of 1/2). So,

(p and q) or (p and r) = false
Thus the distributive law fails

2 Replies

@fresco,

"You asked, does QM follow classical logic ? No."

Again this is and its not true according to your own fuzzy logic which is obviously self refuting...

...dear lord how come ppl like you are scholars and teachers? The insanity of this world is mind boggling!

0 Replies

@Olivier5,

Whether it's very helpful is irrelevant. It is a valid counterexample to your claim.

Consider plane B. Euclidean space is defined as the set of all points in some plane perpendicular to B.

1 Reply

@fresco,

I find it hard to believe that Quantum Mechanics doesn't follow classical logic. The idea that Quantum Mechanics doesn't seems nonsensical. It seems flawed.

Does some contradiction exist in Quantum Mechanics?

2 Replies

@browser32,

You sound as though you had never heard that QM seems 'illogical' in the classical sense !! One wonders where you have been hiding ! If its any consolation, your 'unease' was also expounded by Einstein, but he was technically forced to give way with the proof of Bell's Theorem.

0 Replies

@browser32,

You sound as though you had never heard that QM seems 'illogical' in the classical sense !! One wonders where you have been hiding ! If its any consolation, your 'unease' was also expounded by Einstein, but he was technicallyforced to give way with the proof of Bell's Theorem.

So once again, it appears that you have a lot of basic reading to do both in theories of 'truth', and in the history of QM. Only then will you understand that 'question' was superficial.

1 Reply

@fresco,

Does some contradiction exist in Quantum Mechanics?

2 Replies

@browser32,

Einstein proposed the thought experiment which purported to show that the Heienberg Uncertainty principle led to 'a contradiction'. But the proof of Bell's Theorem allowing the concept of 'non-locality' was the way QM 'resolved' the contradiction. (Ref The Coherence Theory of Truth)
The point is that 'physical' propositions like (a) an electron is a particle and (b) an electron is a wave are 'contradictory', with respect to classical mechanics but not with respect to QM. Once more, this shows that 'contradictions' depend upon paradigmatic context which questions traditional set membership boundaries. QM compounds the issue by making those boundaries probabalistic entities with respect to acts of observation. (Ref: The Correspondence Theory of Truth)
This once again shows the limits of 'classical logic' as cited in the quotes above.

1 Reply

@fresco,

I don't know why you keep bringing up something about set membership. I have not brought up set membership at all until this post. Your point or points regarding set membership don't seem to be relevant. Your focus doesn't seem to be in the right place.

Although electrons have properties of both particles and waves, electrons are particles.(2) The sentence "a single electron is a wave" seems awkward. It seems false.

It seems that even in Quantum Mechanics, when a contradiction is proposed, people try to find a way to resolve the problem so that no contradictions exist.

If there are actual contradictions in Quantum Mechanics, please give me some examples of them.

Works Cited:
(2) https://en.wikipedia.org/wiki/Electron

1 Reply

@browser32,

Potential contradictions in QM are resolved by departing from classical logic.
If you don't know that classical logic is synonymous with the mathematics of set theory then you have no business discussing it. Similarly if you can't be bothered following up suggested references about the limits of clasical logic, don't expect me to be bothered with further replies.

3 Replies

@fresco,

What should have been posted for coherence sake:

fresco wrote:

Potential contradictions in QM are resolved by departing from classical logic, or not.
If you don't know that classical logic is synonymous with the mathematics of set theory then you have no business discussing it, or maybe you do. Similarly if you can't be bothered following up suggested references about the limits of classical logic, don't expect me to be bothered with further replies, but I might do just that.

...imbecile...
Very Happy

0 Replies

@fresco,

I believe classical logic should not be departed from. Any departure from classical logic is just avoiding the problem of potential contradictions. Departure from classical logic is a foolish approach.

I know classical logic is involved with set theory, but I don't believe set membership or set theory is relevant in this case. Your highly abstract talk on set membership and theory has not persuaded me to believe otherwise.

Here is a question I would like answered with a simple yes or no: Does some contradiction exist in Quantum Mechanics?

1 Reply

@browser32,

That is so unschlimbliky though.... :-)

2 Replies

@browser32,

You are wrong, there are fundamental philosophical issues with Set theory "laguaging technology".
Set theory, Finite vs Infinite, Pattern Cycling, that is, Quantity, vs Quality, that is, ACTUAL new patterns, that ad NEW information, are all central core issues for QM and Cosmology.
On QM please check Pilot-Wave Theory for a classical approach.

2 Replies

@Olivier5,

I don't know what you mean by that.

I will ask you the same question I asked @fresco; I request a simple yes or no answer. Does some contradiction exist in Quantum Mechanics?

1 Reply

@Fil Albuquerque,

If the thought experiment known as Schrödinger's Cat implies there is a contradiction in the Copenhagen Interpretation of Quantum Mechanics, why is the Copenhagen Interpretation still so popular?

1 Reply

@browser32,

Politics and career choices...as usual the most trivial reasons...
Academic life is good for the not so stupid among us but equally a nightmare to the real bright ones...

...on your note I also really abhor contradictions.

1 Reply

@Fil Albuquerque,

Maybe people who are involved with the Copenhagen Interpretation, perhaps even including us, aren't meaningfully thinking about what they are doing. I would not want to get highly involved with the Copenhagen Interpretation if it's already been disproved. There are other things I'd rather do.

0 Replies

@Olivier5,

For those wondering where I was trying to go, an "euclidean space" can simply be defined as a space where Euclid's fifth predicate is true.

0 Replies

@Fil Albuquerque,

Fil Albuquerque wrote:

You are wrong, there are fundamental philosophical issues with Set theory "laguaging technology".
Set theory, Finite vs Infinite, Pattern Cycling, that is, Quantity, vs Quality, that is, ACTUAL new patterns, that ad NEW information, are all central core issues for QM and Cosmology.
On QM please check Pilot-Wave Theory for a classical approach.

The classical popular version of Set theory problematic can be seen in the barber's paradox. Should the barber who shaves all people who do not shave themselves shave itself? If the barber decides to shave himself then he should have not done it. Equally if the barber decides to not shave himself immediately it is required that he shaves himself as his group menbership swapped...
Does a master Set which itself is shaped as a triangle containing many smaller triangles belongs to the group counting of triangles? Or does being contained or container changes a fundamental property of what constitutes a requirement for set membership such that it totally changes the equation?

...only stupid ppl are convinced that these problems are well framed and sorted...

0 Replies

Reconciling Schrödinger's Cat with the Principle of Explosion

Related Topics

Quick Links

My Account

able2know