What is the Relationship Between Logic and Quantum Mechanics?

[heusdens]

Originally posted by LW Sleeth
Excellent. I agree logic "works" because it reflects the order/symetry of the universe. It is the same quality that allows math. It works with everything . . . except that which isn't within the boundaries of order and symetry.

By the way, what turned you quantum? Photon bombardment? Blackbody abuse? H??

The universe ain't logical in many respects.

Let's look at the following logical construct.

A is some property
B is some other property

The first rule is that any object having property A does not have property B, and vice versa. So the properties A and B are mutually exclusive.

So, this means that for any object, it can have property A, or property B, or none. But it can't have property A and B simultaniously.

Now let's try this logic for the universe.

Let A be the particle property (having momentum), and let B be the wave property (haveing wavelength). These properties are mutually exclusive.

An electron or other small particles however have shown to have both particle property as wave property.

It seems the universe at fundamental levels isn't working logically.

 

[quantumdude]

Originally posted by heusdens
Let A be the particle property (having momentum), and let B be the wave property (haveing wavelength). These properties are mutually exclusive. An electron or other small particles however have shown to have both particle property as wave property.

The thing is, you cannot observe both simultaneously. This, I think, provides a caveat for the paradox.

 

[heusdens]

Originally posted by Tom
The thing is, you cannot observe both simultaneously. This, I think, provides a caveat for the paradox.

Of course you can, you can perform both experiment at the same time.
Or do you suppose that particles like electrons aren't exactly alike, or that they perform a trick on us, and behave differently in different experiments?

 

[quantumdude]

Originally posted by heusdens
Of course you can, you can perform both experiment at the same time.

No. If you perform, say, Young's 2-slit experiment with a beam of electrons (or photons, neutrons, or whatever), then you will see the wave nature of matter (in this case, the interference pattern), with no data about the particle nature (in this case, the trajectory). If you modify the experiment in such a way as to detect the actual slit the particles pass through (to get some information on the trajectory), then the interference pattern is destroyed.

You can observe either the particle nature or the wave nature in a single experiement, but not both.

Or do you suppose that particles like electrons aren't exactly alike, or that they perform a trick on us, and behave differently in different experiments?

They do behave differently in different experiments.

 

[heusdens]

Originally posted by Tom
No. If you perform, say, Young's 2-slit experiment with a beam of electrons (or photons, neutrons, or whatever), then you will see the wave nature of matter (in this case, the interference pattern), with no data about the particle nature (in this case, the trajectory). If you modify the experiment in such a way as to detect the actual slit the particles pass through (to get some information on the trajectory), then the interference pattern is destroyed.

You can observe either the particle nature or the wave nature in a single experiement, but not both.

for sure one can, it will cost a few dollars more, but hapily there are enough electrons to experiment with. Why not set up both experiments at the same time, and do them simultaniously. They involve 'different' electrons for the experiment, but that is no problem, since all electrons are hold to be identical.
What is the difference between performing the experiment one after another and performing them simultaniously, anyway?

Every electron undergoes just one of the experiments, to have an electron undergo both experiment simultaniously in one experiment would be practically quite difficult. But what difference does that make? maybe one can design an experiment that tests both properies for every electron simultaniously?
I could think of an experiment that does that.

They do behave differently in different experiments.

That is what I stated, indeed. So, electrons don't obey logic.

 

[quantumdude]

Originally posted by heusdens
Why not set up both experiments at the same time, and do them simultaniously. They involve 'different' electrons for the experiment, but that is no problem, since all electrons are hold to be identical. What is the difference between performing the experiment one after another and performing them simultaniously, anyway?

There is a problem: In quantum mechanics, the observer is not separate from the observed. The whole system must be taken into account. Yes, the electrons in the experiment are identical, but the systems (electron+experimental apparatus) are not identical. (edit)I would not expect any object to react the same way to different stimuli, would you?

maybe one can design an experiment that tests both properies for every electron simultaniously?
I could think of an experiment that does that.

OK, which one?

That is what I stated, indeed. So, electrons don't obey logic.

I understood your point to be that the statement "An electron is both a particle and a wave" is of the form (X and ~X), which is always false. You then concluded that electrons do not obey logic because (X and ~X) are, in fact, realized in nature. My objection is that you will never actually observe that contradiction.

That is, unless, you can think of an experiment which reveals both the particle and wave nature of a single electron in one blow.

 

[wuliheron]

He's talking about paraconsistent logic Tom. Here's a website dedicated to a description of the subject.

http://plato.stanford.edu/entries/logic-paraconsistent/

And a short quote from the article:

Consider Bohr's theory of the atom. According to this, an electron orbits the nucleus of the atom without radiating energy. However, according to Maxwell's equations, which formed an integral part of the theory, an electron which is accelerating in orbit must radiate energy. Hence Bohr's account of the behaviour of the atom was inconsistent. Yet, patently, not everything concerning the behavior of electrons was inferred from it. Hence, whatever inference mechanism it was that underlay it, this must have been paraconsistent.

 

[heusdens]

Originally posted by Tom
There is a problem: In quantum mechanics, the observer is not separate from the observed. The whole system must be taken into account. Yes, the electrons in the experiment are identical, but the systems (electron+experimental apparatus) are not identical. (edit)I would not expect any object to react the same way to different stimuli, would you?

Well, it points directly to another flaw in logic, the most basic law of logic, which is the law of identity. There is never a situation in reality in which something is equal to itself. That could only be the case when material existence was not changing in time. But material existence is everlasting change and motion.

OK, which one?

A variation of the Young 2-slit experiment. Between the slit and the detectors that detect the wave form of the electron, one can set up a detector for detecting electron particle behaviour.

You need a beam of electrons that is extended in the plane of the slit. The wave detectors are in a shape of a plane orthogonal to that plane. The particle detectors are placed diagonally to both planes.
So, you have in every horizontal line othogonal to the plane of the slits both detectors placed.
But you might argye against this, cause an individual electron does not particpate in both experiments, but only in one. But if every electron is equal to every other electron, this would not make any difference, because there are electrons that participate which are above or beneath (in the directions of the slit) the diagonal particle detector, that should be in the same state as the one that is detected in the diagonal particle detector.

I understood your point to be that the statement "An electron is both a particle and a wave" is of the form (X and ~X), which is always false. You then concluded that electrons do not obey logic because (X and ~X) are, in fact, realized in nature. My objection is that you will never actually observe that contradiction.

That is, unless, you can think of an experiment which reveals both the particle and wave nature of a single electron in one blow.

If the experiment works, who knows?

But my basic point is that the rules of logic aren't really applicable to the way nature works.

For example the law of Identity (A=A).

Is a pound of sugar equal to a pound of sugar? On first instance they seem the same, but when having a closer look, you see differences.

Is a proton equal to a proton? A proton in the nucleus is always in the process of change due to the nuclear strong force that binds the nucleus together. A proton is at one moment a proton, and a neutrino on the other moment. So a proton is only a proton if you stop the time, but then a proton does not exist.

 

[drag]

Greetings !

Originally posted by heusdens
A variation of the Young 2-slit experiment. Between the slit and the detectors that detect the wave form of the electron, one can set up a detector for detecting electron particle behaviour.

You need a beam of electrons that is extended in the plane of the slit. The wave detectors are in a shape of a plane orthogonal to that plane. The particle detectors are placed diagonally to both planes.
So, you have in every horizontal line othogonal to the plane of the slits both detectors placed.
But you might argye against this, cause an individual electron does not particpate in both experiments, but only in one. But if every electron is equal to every other electron, this would not make any difference, because there are electrons that participate which are above or beneath (in the directions of the slit) the diagonal particle detector, that should be in the same state as the one that is detected in the diagonal particle detector.

If I understand you correctly you want
to probe some electrons and not others.
Fine. If you do that then some electrons
will show interference patterns and others
won't. But those are different electrons.

Originally posted by heusdens
But my basic point is that the rules of logic aren't really applicable to the way nature works.

The popular accepted rules of the applied reasoning
system called logic appear to be violated in a number
of ways by QM, indeed.

Violations include amongst other problems: effect
before cause, lack of locality (instant action),
lack of identity - particles can not be
individually distinguished between each other
in an experiment and the fact(an older problem)
that EM waves are fluctuations in "nothing".

However, there are two things you should take
into account: First, what we call logic is
just some particular applied reasoning system,
we can have others instead. Second, you are
faced with the choice of either abandoning the
basic assumptions of all other physical theories
or not trusting QM to be a real representation
of what's goin' on. The fact that QM (despite being
the most accurate physical theory so far) disagrees
with GR is another point against it's interpretation
(no one's arguing with the actual results).

The choice is yours...

Live long and prosper.

 

[heusdens]

Originally posted by drag
Greetings !

If I understand you correctly you want
to probe some electrons and not others.
Fine. If you do that then some electrons
will show interference patterns and others
won't. But those are different electrons.

Like I said, some electrons will be captured in one detector, and other in the other detector, but not can be detected in both detectors.
But the electrons lined up in the same direction as the slit, should be called identical, since they show identical behaviour. Unless you say that an electron in a same state is not equal to an electron in that same state.

You choose.

The popular accepted rules of the applied reasoning
system called logic appear to be violated in a number
of ways by QM, indeed.

Violations include amongst other problems: effect
before cause, lack of locality (instant action),
lack of identity - particles can not be
individually distinguished between each other
in an experiment and the fact(an older problem)
that EM waves are fluctuations in "nothing".

However, there are two things you should take
into account: First, what we call logic is
just some particular applied reasoning system,
we can have others instead. Second, you are
faced with the choice of either abandoning the
basic assumptions of all other physical theories
or not trusting QM to be a real representation
of what's goin' on. The fact that QM (despite being
the most accurate physical theory so far) disagrees
with GR is another point against it's interpretation
(no one's arguing with the actual results).

The choice is yours...

Live long and prosper.

My argument that there is at least a difficulty in applying logic to the real world. I don't suggest we would want to abandon QM or logic.

That on the fundamental levels of reality there appear to be contradictions is just a fact I would suppose. We should apply proper reasoning to accommodate for these contradictions.

To me the most fit form of reasoning we have come up with so far is dialectical materialism, which fruitfully deals with these contradictions.

 

[FZ+]

Maybe we can make a distinction between logic, which is a tool we use to see what follows from another, and intuitive reasoning, which is based on instinct a form of knowledge? For while instinct is an imperfect accumulation of basic "common sense", logic is a manifestation of the universe.

Just my 2 cents.