Quantum Mechanics: Paradoxical?

[drag]

Greetings !

Originally posted by wuliheron
Exactly what the HUP describes is the huge
debate in QM. To claim you have the answer
that has evaded physicists for over a hundred
years is rather arrogant to say the least.

What are you talking about ?!
I wasn't talking of any interpretation !
I was talking about the well defined and known
formulas energy/time and mommentum/location
uncertainties. These are strictly defined
through the theory's equations.

Originally posted by wuliheron
That everything in physics may ultimately be
magical and without a cause implies paradox,
thus it is exactly what the discussion is about.

Nope, we're discussing Mentat's definition not the PoE.

Originally posted by wuliheron
Ahkron has attempted to redefine the concept of
"truth" in classical Aristotelian logic as
"reality" in my opinion, but this defeats at
least half the purpose of logic. Logic is not
aimed so much at affirming or describing the truth,
but instead is more pointedly aimed at discerning
the truth.

Aristotle himself used absurdities to support
the validity of his logic. These absurdities he
used are essentially no different from the ones
described by QM, that is, contradictions and
paradoxes. Thus either we decide Aristotle was
just speaking in paradoxes and we can interpret
his logic and QM anyway we want or we assume he
was attempting to create a useful method of
analysis as he clearly said he was and as all
his actions indicate he was.

I strongly agree with what you're saying about
the purpose of an r.s. and logic in particular.

You'll notice that I aksed ahrkron about his
definition of "normal" logic. And now that you
come to remind us of the main purpose of an r.s.
I think I'll return to my original opinion -
that QM violates "normal" logic.

I respect ahrkron's "premises" argument but
what's the point really in having an r.s. that
can change its premises like that ? If you
want an r.s. that can tell you something about
the Universe - be of use, you need to limmit -
focus it as much as possible. And if it fails -
get a new one.

Live long and prosper.

 

[wuliheron]

Originally posted by drag
Greetings !

What are you talking about ?!
I wasn't talking of any interpretation !
I was talking about the well defined and known
formulas energy/time and mommentum/location
uncertainties. These are strictly defined
through the theory's equations.

This is what you wrote:

Ha ! That is NOT what we're discussing.

The HUP is a BASIC principle of QM. It is as
basic as the particles and space-time for example
in other theories. Hence, it is NOT "magic"
unless you consider all the other basic things
in physics to be magical too(which may be the
case, but was not part of this discussion).

Instantaneous teleportation through walls, being in two places at the same time, etc. is magic. Sure, the equations are nice and quite respectable, but the things they imply are outrageous. The HUP itself is the center of all this attention because of its indeterminacy.

Nope, we're discussing Mentat's definition not the PoE.

Where have you been. This is what Mentat defined as a paradox:

First let me define my use of the word paradox, in this thread. A paradox is a self-contradictory statement, or one that cannot be true, but also cannot be false.

By definition anything that defies such a strict Aristotelian logic is either axiomatically false or magical.

I respect ahrkron's "premises" argument but
what's the point really in having an r.s. that
can change its premises like that ? If you
want an r.s. that can tell you something about
the Universe - be of use, you need to limmit -
focus it as much as possible. And if it fails -
get a new one.

Or, you simply need to be flexible. This is what Quantum Mechanics provides through the ambiguity of Indetermancy. Describes not only the more mechanical and predictable Newtonian Mechanics of everyday existence, but also the bizarre realm of the wavefunction.

 

[ahrkron]

Originally posted by drag
I strongly agree with what you're saying about
the purpose of an r.s. and logic in particular.

What does "r.s." stand for?
(reasoning system?)

You'll notice that I aksed ahrkron about his definition of "normal" logic.

First order logic (propositional logic plus quantifiers).

I think I'll return to my original opinion -
that QM violates "normal" logic.

I think you are confusing logic (the structural rules to make inferences) with content (which has to do with the premises used).

The logic used in QM is not "abnormal" in any sense. It produces inferences in exactly the same way as your everyday logic. The difference is in the realization that many things we usually assume (i.e., use as premises) in everyday life do not hold for small objects.

A simple example of that is that, for everyday objects, it is true that

A system has to be in a single definite state at all times

so that, when you learn that

System A has only two possible states: A1 or A2

and that

Today, system A is on state A2

You can conclude that

Today, system A is not on state A1

In QM, on the other hand, the first assumption (A system has to be in a single definite state at all times) does not hold.

Such being the case, it is clear that even if you learn that the other two premises are true, you still cannot reach the same conclusion.

This is not because a different "logic" is used, but because many of the "starting assumptions" we normally use in everyday life are not applicable at the high energies/small scales of the quantum realm.

I respect ahrkron's "premises" argument but what's the point really in having an r.s. that can change its premises like that?

Science works like this. It tries to extract the minimum set of assumptions that can account for observed phenomena. When new data is gathered that contradicts the current model, such assumptions are scrutinized and modified if necessary (think of C violation, P violation and CP violation: all of them were thought to be valid assumptions until experiments showed otherwise).

... actually, the one thing that does not change is the inference system.

 

[wuliheron]

Originally posted by ahrkron

Science works like this. It tries to extract the minimum set of assumptions that can account for observed phenomena. When new data is gathered that contradicts the current model, such assumptions are scrutinized and modified if necessary (think of C violation, P violation and CP violation: all of them were thought to be valid assumptions until experiments showed otherwise).

... actually, the one thing that does not change is the inference system. [/B]

Exactly, but it is an inference system ultimately based on Indeterminacy or paradox.

 

[ahrkron]

Originally posted by wuliheron
Exactly, but it is an inference system ultimately based on Indeterminacy or paradox.

Not at all. The indeteminacy is not even an assumption!

The assumptions of QM are statements about hermitian operators, eigenvalues, measurements and probabilities. They are all (both the postulates and the concepts they're built upon) well defined and unambiguous.

The HUP can be derived from these postulates, and it does not mean that measurements are "self-contradictory"; in a sense, quite the contrary: they show that, upon measurement, a quantum object will show either its "wave" aspect or its "particle" aspect, not both.

 

[ahrkron]

Originally posted by wuliheron
Exactly, but it is an inference system ultimately based on Indeterminacy or paradox.

Also, I tried to make clear that the inference system has nothing to do with the HUP.

To make it clearer: the inference system used to develop, learn and do research on QM is normal everyday logic (not even modal, fuzzy, paraconsistent or any other sort of fancy logic).

The difference is not on the reasoning system, but in the initial assumptions. It is those assumptions that allow for conclusions that conflict our everyday experiences.

How do you think a researcher makes inferences about QM? by saying "here, I conclude that the answer is YES, but since QM allows contradictions, then it is also NO"? or "then, by paradox, the result is..."?

Predictions, models and interpretations are developed using formal reasoning of the same kind you find in any calculus or geometry investigation, without any reference (or assumption) about the "paradoxical" character of some people's account of the theory.

 

[wuliheron]

Originally posted by ahrkron
Not at all. The indeteminacy is not even an assumption!

The assumptions of QM are statements about hermitian operators, eigenvalues, measurements and probabilities. They are all (both the postulates and the concepts they're built upon) well defined and unambiguous.

The HUP can be derived from these postulates, and it does not mean that measurements are "self-contradictory"; in a sense, quite the contrary: they show that, upon measurement, a quantum object will show either its "wave" aspect or its "particle" aspect, not both.

Theoretically, there are only two possibilities. Either the wavefunction is a crazy unimaginable state like shrondenger's cat or a new universe is created for everything that doesn't happen in this one. If either one of those makes perfect sense to you there is a rubber room waiting for you somewhere.

 

[ahrkron]

Originally posted by wuliheron
Either the wavefunction is a crazy unimaginable state like shrondenger's cat

The "magic" and "craziness" of QM is not on the wavefunction, but in the effect that a measurement has over it and, mainly, in the unjustified expectation that quantum systems should agree with classical mental models.

or a new universe is created for everything that doesn't happen in this one.

Not necessarily, but even if that was the case, scientific models may be surprising and (again) very different from your everyday-life ideas, but why do you think models are proposed (and later on accepted)? It is precisely because, once all details are investigated thoroughly, they do make sense of known experimental results. That is precisely what science is all about.

Again, the fact that QM is seems to conflict daily life experiences comes from the fact that if you assume daily-life rules to work on atoms, then calculate what you should see, and then make an experiment, the result of the experiment does not match your calculation.

Once you make many more experiments and find a model for how the atom behaves, you end up:
1. understanding that there were many hidden assumptions on the original calculation,
2. realizing that those were unwarranted assumtions, that do not hold at quantum level,
3. finding that using the right assumptions for the behavior of quanta, not only the original experiment makes sense, but also many other macroscopic behaviors are explained.

It is differerent from what "common-sense" expects, but it does make sense.

Don't forget that "common-sense" or "normal-logic" is basically a set of assumptions based on a very limited set of conditions (small velocities, small energies, "meduim" sizes, low temperatures, low pressures, small gravitational fields) and filtered through a very useful, but also very limited, set of perceptual mechanisms. The fact that many of those assumptions are wrong should not be a big surprise, neither be food for assuming that the conflict comes from "essential paradoxes". The conflict is a rather natural result of the limited range of what constitutes the human perceptions.

 

[wuliheron]

Originally posted by ahrkron

The "magic" and "craziness" of QM is not on the wavefunction, but in the effect that a measurement has over it and, mainly, in the unjustified expectation that quantum systems should agree with classical mental models.

That assumes that the Many Worlds theory is false, which has not been proven. According to Quantum Decoherence and the Many Worlds theory observers and measurements are irrelevent. All of the possible states are present in the system to begin with and one is realized locally upon interacting with anything.

Not necessarily, but even if that was the case, scientific models may be surprising and (again) very different from your everyday-life ideas, but why do you think models are proposed (and later on accepted)? It is precisely because, once all details are investigated thoroughly, they do make sense of known experimental results. That is precisely what science is all about.

Again, the fact that QM is seems to conflict daily life experiences comes from the fact that if you assume daily-life rules to work on atoms, then calculate what you should see, and then make an experiment, the result of the experiment does not match your calculation.

No, it is not merely everyday experience QM conflicts with, it conflicts with formal logic. This is a much deeper issue than simply conflicting with what we are used to. The Earth is round even though for millennia we thought it was flat, that is a simple conflict with human perception of reality but QM is another animal entirely. It insists in a sense that the Earth is both round and flat at the same time or a new Earth is created everytime and interaction takes place.

It may be that theories like M-theory may eventually provide some kind of reasonable explanation for QM, but it hasn't happened yet.

 

[drag]

Greetings !

Originally posted by ahrkron
What does "r.s." stand for?
(reasoning system?)

Yep, too long to write it all the time.

Originally posted by ahrkron
First order logic (propositional logic plus quantifiers).

I ask forgiveness for my ignorance, but I'm not
aware of the official definitions of these terms yet.
(Tom suggested this Karl Popper Web site, but I didn't
have time to take a serious look at it.)

Originally posted by ahrkron
I think you are confusing logic (the structural rules to make inferences) with content (which has to do with the premises used).

How can you have independent structural rules ?

The PoE makes any absolute rules impossible.
It seems useful and more potenitally rewarding
to me to limmit and focus one's r.s. as much as
possible - thus achieveing maximum results -
exploitation of each system. (Of course, when the
system eventually leads to a problem(as it must )
it's probably more usefull to ty other systems.)

I realize that my ignorance is evident here
because the distinction you indicated - structural
rules/inferences is probably the one currently accepted,
but eventually I can't view such distinction as
more than historical scientific development based or
in other words sentimental attachment - because the
discoveries of the past are not an indication for
future discoveries(as was shown many times).

Originally posted by ahrkron
The logic used in QM is not "abnormal" in any sense.
It produces inferences in exactly the same way as
your everyday logic. The difference is in the
realization that many things we usually assume
(i.e., use as premises) in everyday life do not
hold for small objects.

In my case, these premises are part of the r.s.
I would call "normal" logic. In "my QM" logic the
premises are those of QM and hence everything (the
parts of QM)make perfect sense.

"Simplicity is the ultimate sophistication."
Leonardo Da Vinci

Live long and prosper.

 

[ahrkron]

Originally posted by wuliheron
That assumes that the Many Worlds theory is false

No, it doesn't. The many worlds interpretation does assume an event at the time of measurement.

All of the possible states are present in the system to begin with and one is realized locally upon interacting with anything.

That is what I am talking about. The wavefunction is not "crazy". It just follows a set of rules different from the ones we used to train our everyday-intuition. It is good that you bring up QDecoherence, since it is an interpretation that makes things even more "normal": if true, then the reduction of the wavefunction happens because of the instability of coherent quantum states, instead of anything having to do with an "observer".

No, it is not merely everyday experience QM conflicts with, it conflicts with formal logic.

It does not. No matter how many times you repeat it, it won't become true.

 

[wuliheron]

Originally posted by ahrkron
No, it doesn't. The many worlds interpretation does assume an event at the time of measurement.

Yes, but these events do not collapse a wavefunction in the Many Worlds theory as other interpretations insist they do. The act of measurement/observation does not change the logic of the system from Quantum logic to classical, the logic remains classical throughout.

That is what I am talking about. The wavefunction is not "crazy". It just follows a set of rules different from the ones we used to train our everyday-intuition. It is good that you bring up QDecoherence, since it is an interpretation that makes things even more "normal": if true, then the reduction of the wavefunction happens because of the instability of coherent quantum states, instead of anything having to do with an "observer".

I'm sorry, but words such as "crazy", "supernatural", "paradox" etc. have meaning only because people give them meaning. Those meanings are based on human perception, not mathematical consistency or experimental results. Often QM is compared to Alice in Wonderland precisely because of its craziness. Mathematically the stories may be self-consistent just as the artwork of MC Echer is self-consistent and these mathematics may closely parallel those of QM, but they are crazy nonetheless by definition.

quote:
--------------------------------------------------------------------------------
No, it is not merely everyday experience QM conflicts with, it conflicts with formal logic.
--------------------------------------------------------------------------------
It does not. No matter how many times you repeat it, it won't become true.

Every explanation for QM incorporates nonlocal effects which defy the true or false, here or there, black or white and-never-the-two-shall-meet criteria of classical logic. No matter how many times you deny this, it remains a widely accepted fact within the physics community.

 

[Lifegazer]

Originally posted by ahrkron
QM is definitely not paradoxical in the predictions it makes. If it was able to produce mutually contradicting predictions, it would have no use as a physical theory.

I think you're missing the point here. Imagine, if you will, that all cats turned into frogs at midnight for several minutes. Now, the fact that we can accurately predict that my cat will start croaking at midnight does not mean that there isn't something 'mysterious' going on within that event itself.

 

[Mentat]

I think I'm going to agree with Ahrkron (sp?) on this issue. That's not to say that others haven't presented meritable arguments. It's just that people seem to keep sticking to "common sense" reasoning. Obviously this is not always a good idea. "Common sense" is for common circumstance, and the Quantum world doesn't meet that criteria.

 

[Lifegazer]

Originally posted by Mentat
I think I'm going to agree with Ahrkron (sp?) on this issue. That's not to say that others haven't presented meritable arguments. It's just that people seem to keep sticking to "common sense" reasoning. Obviously this is not always a good idea. "Common sense" is for common circumstance, and the Quantum world doesn't meet that criteria.

It's strange how you agree with Ahrkron, and then state that QM doesn't appeal to common-sense. Did I miss something?

 

[Mentat]

Originally posted by Lifegazer
It's strange how you agree with Ahrkron, and then state that QM doesn't appeal to common-sense. Did I miss something?

Possibly. You see, I said that it didn't appeal to common sense. Then I said that common sense is for common circumstance. Then I said that Quantum Mechanics doesn't deal with common circumstances. Conclusion: A different line of reasoning, then that which is "common", is required to understand the Quantum world. This new line of reasoning is still logical (or so it seems to be, after having read Arkhron's posts), it is just better suited for dealing with the "uncommon".

 

[Eyesee]

Originally posted by ahrkron
The "magic" and "craziness" of QM is not on the wavefunction, but in the effect that a measurement has over it and, mainly, in the unjustified expectation that quantum systems should agree with classical mental models.



Not necessarily, but even if that was the case, scientific models may be surprising and (again) very different from your everyday-life ideas, but why do you think models are proposed (and later on accepted)? It is precisely because, once all details are investigated thoroughly, they do make sense of known experimental results. That is precisely what science is all about.

Again, the fact that QM is seems to conflict daily life experiences comes from the fact that if you assume daily-life rules to work on atoms, then calculate what you should see, and then make an experiment, the result of the experiment does not match your calculation.

Once you make many more experiments and find a model for how the atom behaves, you end up:
1. understanding that there were many hidden assumptions on the original calculation,
2. realizing that those were unwarranted assumtions, that do not hold at quantum level,
3. finding that using the right assumptions for the behavior of quanta, not only the original experiment makes sense, but also many other macroscopic behaviors are explained.

It is differerent from what "common-sense" expects, but it does make sense.

Don't forget that "common-sense" or "normal-logic" is basically a set of assumptions based on a very limited set of conditions (small velocities, small energies, "meduim" sizes, low temperatures, low pressures, small gravitational fields) and filtered through a very useful, but also very limited, set of perceptual mechanisms. The fact that many of those assumptions are wrong should not be a big surprise, neither be food for assuming that the conflict comes from "essential paradoxes". The conflict is a rather natural result of the limited range of what constitutes the human perceptions.

How can a particle know how to interact with any other particle if it isn't even sure of who it is? We may be UNCERTAIN about the particle's state functions but I think it knows very well who it is at every moment in time. I've got three words for you: Einstein's hidden variables.

 

[Mentat]

Originally posted by Eyesee
How can a particle know how to interact with any other particle if it isn't even sure of who it is? We may be UNCERTAIN about the particle's state functions but I think it knows very well who it is at every moment in time. I've got three words for you: Einstein's hidden variables.

You think the particle knows something? I have a question for you, why does it take our complex assortement of particles (our brains) to create a consciousness that we exist, while other animals (who also have - slightly less complex - assortments of particles) do not have this level of consciousness?

 

[ahrkron]

Originally posted by Eyesee I've got three words for you: Einstein's hidden variables.

The problem with those three words are two other words: Bell's theorem.

 

[Eyesee]

Originally posted by Mentat
You think the particle knows something? I have a question for you, why does it take our complex assortement of particles (our brains) to create a consciousness that we exist, while other animals (who also have - slightly less complex - assortments of particles) do not have this level of consciousness?

I find your rebuttal question inadequate. My question was directed at the fundamental properties of the particles themselves whereas yours address the different arrangements of particles resulting in different properties- the former is about apples, the latter, of orangutangs. And even then, I think you answered your own question in your question: our assortment of particles is different than other animals- it would only be amazing if we were the same and not different. Would you expect your car keys to open the front door of your house?

So, again, how can a particle know how to behave if it wasn't sure of itself? If you were an electron and you weren't sure you were going east or west, how can you respond to some proton that approaches you? As a matter of fact, according to the schizophrenic interpretation of the universe given by QM, the proton itself wouldn't be sure if it was approaching the electron from the east or west either, so how can momentum between this simple system of particles be conserved 100% of the time?

------------------------------------------------------------
The universe exists for Helen Keller the same way as it does for every one else.

 

[ahrkron]

Originally posted by Eyesee
So, again, how can a particle know how to behave if it wasn't sure of itself? If you were an electron and you weren't sure you were going east or west, how can you respond to some proton that approaches you? As a matter of fact, according to the schizophrenic interpretation of the universe given by QM, the proton itself wouldn't be sure if it was approaching the electron from the east or west either, so how can momentum between this simple system of particles be conserved 100% of the time?

Wavefunctions and quantum fields are well defined (notice I am not talking about what we call "particles"). They do have many symmetries, some of which imply that a subset of our interactions with them (those we call "experiments") conserve momentum and other quantities.

The confusion arises when we try to use categories ("electron", "wave", "trajectory") that are not well suited for their description.

 

[Eyesee]

Originally posted by ahrkron
Wavefunctions and quantum fields are well defined (notice I am not talking about what we call "particles"). They do have many symmetries, some of which imply that a subset of our interactions with them (those we call "experiments") conserve momentum and other quantities.

The confusion arises when we try to use categories ("electron", "wave", "trajectory") that are not well suited for their description.

Ok, this reply makes much sense.

 

[drag]

Greetings !

Originally posted by Mentat
Possibly. You see, I said that it didn't
appeal to common sense. Then I said that common
sense is for common circumstance. Then I said
that Quantum Mechanics doesn't deal with
common circumstances. Conclusion: A different
line of reasoning, then that which is "common",
is required to understand the Quantum world.
This new line of reasoning is still logical
(or so it seems to be, after having read
Arkhron's posts), it is just better suited
for dealing with the "uncommon".

What does "logical" mean to you ?
I proposed a nearly similar solution. However,
my solution is that of a totally different
reasoning system (different common sense).

The difference is that in that case my definition
of "logical" is just that the new r.s. does
not result in internal paradoxes - it is consistent.

Ahrkron's definition, with which you claim to agree,
is that "logical" means more than that - there
are some general criteria which define what
is "logical" and this new r.s. is the same in this
respect as that what you call "common sense".

However, is there anything you can be certain of
in the Universe to create such criteria ?
Hasn't reality shown us repeatedly that what
we consider absolute and certain is not really so.
(I should point out that my current ignorance
about what ahrkron called "structural rules" for
"logical" systems may in fact mean that they're
the same as my self consistency consideration above
and nothing more, and I simply didn't know that.
But, all those rules and stuff he mentioned sounds
like too many limmitations to me.
What can I say ? I'm foolish and I'll have to study
this stuff before I can express a really educated
opinion on this.)

Originally posted by Eyesee
How can a particle know how to interact with
any other particle if it isn't even sure
of who it is? We may be UNCERTAIN about the
particle's state functions but I think it
knows very well who it is at every moment
in time. I've got three words for you:
Einstein's hidden variables.

QM crushes the classical physics trait
of individuality. It is not possible to
distinguish between similar particles
more than it is possible to distinguish
between individual water drops in the ocean.

"Simplicity is the ultimate sophistication."
Leonardo Da Vinci

Live long and prosper.

 

[Mentat]

Originally posted by Eyesee
I find your rebuttal question inadequate. My question was directed at the fundamental properties of the particles themselves whereas yours address the different arrangements of particles resulting in different properties- the former is about apples, the latter, of orangutangs. And even then, I think you answered your own question in your question: our assortment of particles is different than other animals- it would only be amazing if we were the same and not different. Would you expect your car keys to open the front door of your house?

So, again, how can a particle know how to behave if it wasn't sure of itself? If you were an electron and you weren't sure you were going east or west, how can you respond to some proton that approaches you? As a matter of fact, according to the schizophrenic interpretation of the universe given by QM, the proton itself wouldn't be sure if it was approaching the electron from the east or west either, so how can momentum between this simple system of particles be conserved 100% of the time?

------------------------------------------------------------
The universe exists for Helen Keller the same way as it does for every one else.

You may have missed the point of my rhetorical question (afore-quoted), so I will try to be more clear: Why do you think that a particle knows something? You keep speaking of particles as individual, conscious, entities - when they are, in fact, neither individual or conscious.

 

[Mentat]

Originally posted by drag
Greetings !

What does "logical" mean to you ?
I proposed a nearly similar solution. However,
my solution is that of a totally different
reasoning system (different common sense).

"Logic" is the use of reasoning systems (to be absolutely basic). So, it doesn't matter what reasoning system you use, or what premise it's based on, you still have something "logical".

Ahrkron's definition, with which you claim to agree,
is that "logical" means more than that - there
are some general criteria which define what
is "logical" and this new r.s. is the same in this
respect as that what you call "common sense".

Yes, it's in the same respect as "common sense" because it's the same reasoning system, merely without the premise: "an individual object can exist in only one state, at any given time".