# Do superpositions violate conventional logic (philosophy)?

I recently read a research summary about using magnetic fields to briefly maintain quantum states in relation to quantum computing. The article makes reference to "a" simultaneously being "a" and "not 'a'".

I'm left wondering how the concept of superposition is reconciled with conventional notions of logic in philosophy. Also, does the standard notion of logic collapse if there is no clear reconciliation (i.e. are we then forced to admit to the fallibility of conventional logic)?

My only thought thus far is found in browsing the Copenhagen interpretation (which I admittedly don't clearly understand the mechanics of). The Copenhagen interpretation inspires the thought that particles have at least two states and can therefore be two things simultaneously. Additionally, there is no recognizable logical violation if our measuring apparatuses are not specific/sensitive enough to accurately perceive logic in the quantum universe.

Forgive my ignorance if this question has already been addressed,

Ambler

*Edit: In retrospect, logic is dependent on current paradigms. If logic does fail to predict real world circumstances, one changes the definition of "logic" rather than collapsing the concept. To allow the concept of logic to collapse would essentially allow for deductions to be considered uncritically "true".

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## Answers and Replies

Classical thinking applies to quantum theory as low speed experience applies to special relativity.

There are two approaches to this issue.

One opts for 'quantum logic' or 'fuzzy logic', or other logics different than standard one (wiki on them!).

Second approach (definitely dominating) is to use standard boolean logic to describe quantum phenomena in the way similar to that as this logic is used in mathematics operating on real numbers, or as boolean logic is a foundation of probability theory.

The Copenhagen interpretation inspires the thought that particles have at least two states and can therefore be two things simultaneously.
Really? I always took Copenhagen interpretation as: "Don't think about particles except of very moment of measurement", so there are not even a single thing until measured.

In retrospect, logic is dependent on current paradigms. If logic does fail to predict real world circumstances, one changes the definition of "logic" rather than collapsing the concept.
Could you elaborate this thought a bit? Esp. in historical view, how 'paradigms' was influencing the logic?

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Xts, I cannot sensibly refute your understanding of the Copenhagen interpretation. My comments and questions clearly reflect my limited knowledge of physics (and philosophy). That being said, I must introduce this reply by admitting that even after a bit of research, I can't comprehend how quantum computers can use two state (boolean) logic to conduct more operations per cycle than a transistor based chip (although I can see how QC could conduct more operations per unit of energy). Why doesn't applying Boolean algebra to quantum computing necessarily discard the third bit as a processing unit?

My claim that logic is based on current paradigms is a reference to the notion that reality is limited by the perceptive abilities of the observer. Based on an article I've skimmed in Skeptic Magazine, I believe that various physicists are referring to this philosophical concept as MDR. A new understanding of a concept can change the nature of human thinking and ultimately expand the scope of human thinking (for example, the formal understanding of abstract language). Logical contradictions in quantum physics can force such a redefinition of the deductive capacity of logic (because conventional logic dictates that something is either "a" or "not a"). Philosophically speaking, there may be an unrealized but more descriptive "logic" beyond human comprehension due to the modern non-necessity (or intellectual limitations) of thinking about certain abstracted concepts.

Again I speak as an untrained logician when I say that "fuzzy logic" doesn't strike me as applicable to logic in quantum computing. In my understanding of Quantum superposition logical paradoxes can exist in physical reality. Fuzzy logic does not appear to me as capable of producing logically contradictory results - instead fuzzy logic takes into account partial values and mistakenly refers to these partial values as distinct states. Alternately, superposition does create a distinct third state in apparent contradiction to conventional logic.

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Why is it so illogical to say that an experiment has a statistical probability associated with each outcome before measurement?

Why is it so illogical to say that an experiment has a statistical probability associated with each outcome before measurement?

Lost, thank you for reminding me of the concept of probabilities in logic. I believe I see your point: all things are possible however unlikely an outcome may be. I'll need a bit of time to consider the ramifications of this in relation to my initial posting. However, for the time being I'm going to occupy my mind with something other than mathematics and its retarded little brother; philosophy.

I see you took seriously Kuhn's ideas about 'paradigms' and 'concepts' and revolutions in thinking. Nothing more wrong!

There are no logical contradictions in QM. QM is built upon classical mathematics, whose very foundation is classical logic. What may seem to contradict logic are some narrations used when speaking about QM phenomena. But if those narrations contradict logic it means that narrations are erroneous, not the logic. You may describe the phonomena using different narration, staying consistent with old good binary logic. The same as you may enjoy half filled glass of wine without falling into any contradiction with logic (either empty or not empty?) You must just have some intuitions about real numbers, formalized by Cantor on the basis of ordinary binary logic.

"fuzzy logic" doesn't strike me as applicable to logic in quantum computing
Right. But 'Quantum logic' may be probably used. Anyway - my Occamian soul tells me not to play with logic - it is much easier and simpler to express QM in classical mathematics.
Logic is abstract, deductive, mathematical knowledge, independent from the Universe. Logic originates not in the external world, but rather in our language and rules how can we transform sentences.

In my understanding of Quantum superposition logical paradoxes can exist in physical reality.
Ouch!!! You dug out the stinking cadaver of scholastic disputes: 'what the reality is?'
If you adopt minimalistic empirical approach ('reality' is what you may touch) - in QM: 'reality' is an experiment outcome, while everything else (wavefunctions, etc.) are just mathematical tools useful to predict those outcomes, then you never fail in logical paradoxes.

There are no logical contradictions in QM.

There are some contradictions. For example how can the definite quanta of the energy in a wave (a photon for example), the smallest measurable energy, so discrete as to never be found in two places at once and never be half measured, demonstrate interference with itself?

There are some contradictions. For example how can the definite quanta of the energy in a wave (a photon for example), the smallest measurable energy, so discrete as to never be found in two places at once and never be half measured, demonstrate interference with itself?
Yeah? May you demonstrate self-contradiction in this sentence without using preassumption about real existence of the particle along its path?

QM says nothing about 'interference with itself'. It says, that as particles are emitted at one point, and detected on a screen, they form a fringe pattern if we put double slit in between source and screen. QM allows to predict that pattern. That's all.
Where is a self-contradiction or contradiction to logic?

Maybe rather your narration about 'interfering with itself' (although common when talking about QM) contradicts your other intuitions you put under terms such as 'particle', 'interference', etc?

What is more non-logical in pattern formed by electrons than in pattern of waves on a pond? The mathematics behind those two is almost the same.

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Yeah? May you demonstrate self-contradiction in this sentence without using preassumption about real existence of the particle along its path?

QM says nothing about 'interference with itself'. It says, that as particles are emitted at one point, and detected on a screen, they form a fringe pattern if we put double slit in between source and screen. QM allows to predict that pattern. That's all.
Where is a self-contradiction or contradiction to logic?

Maybe rather your narration about 'interfering with itself' (although common when talking about QM) contradicts your other intuitions you put under terms such as 'particle', 'interference', etc?

What is more non-logical in pattern formed by electrons than in pattern of waves on a pond? The mathematics behind those two is almost the same.

An electron is not described as a wave at all. It's motion may be described by a non-physical wave function. A wave in a pond is a physical wave.

The logical conclusion to the pattern is that there was interference. The logical conclusion to discreetness is that it can't interfere with itself.

Agreed, our logic should be found to be wrong when these things are better understood. But currently certain QM experiments defy common logic.

Yeah? May you demonstrate self-contradiction in this sentence without using preassumption about real existence of the particle along its path?

If that is true, the level of detail and consistency of experience are really exemplary.

Why is it so illogical to say that an experiment has a statistical probability associated with each outcome before measurement?

So probability is more fundamental than anything else(e.g. forces, interactions, etc.)? As in the statement - "probability holds everything together"

The logical conclusion to discreetness is that it can't interfere with itself.
May you show some reasoning behind that?
Better than induction from common experience that pebbles, rabbits and especially large mammooths never form interference fringes? (Forget for a moment about sand on a beach, which actually form them...)
Is logic wrong, or maybe rather your understanding of the word 'discrete'?

So probability is more fundamental than anything else(e.g. forces, interactions, etc.)?
I don't like such sentences, as no one ever defined precisely what 'being more fundamental' means.

I don't like such sentences, as no one ever defined precisely what 'being more fundamental' means.

In a number of interpretations observables are resultant from measurement/observation. Hence, forces/interactions would be defined as secondary concepts, i.e. not fundamental.

xts said:
Is logic wrong, or maybe rather your understanding of the word 'discrete'?

Is your understanding of the term 'discrete' much different than everybody else's?

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In a number of interpretations observables are resultant from measurement/observation. Hence, forces/interactions would be defined as secondary concepts, i.e. not fundamental.
That's a slippery way, because that is not probability which is fundamental, but rather act of observation. Probability is not much more fundamental for my taste than wave function itself or forces. Which of them are more and which are less fundamental?
Is your understanding of the term 'discrete' much different than everybody else's?
Mine? I think it is pretty consistent with Oxford dictionary ('individually distinct, discontinuous'). There in nothing in it which could prohibit forming fringe patterns.

That's a slippery way, because that is not probability which is fundamental, but rather act of observation.

Sure, but i said "more fundamental", not fundamental. A statement like "observation is fundamental" is a step further than my statement "probability is more fundamental than forces/interactions".

Probability is not much more fundamental for my taste than wave function itself or forces. Which of them are more and which are less fundamental?

Momentum is an observable of the wavefunction, hence wavefunction and probability must be more fundamental than force. That is unless you are insisting on a kind of quantum realism that is unassailable.

Mine? I think it is pretty consistent with Oxford dictionary ('individually distinct, discontinuous'). There in nothing in it which could prohibit forming fringe patterns.

Fringle patterns to infinity are not consistent with Oxford's definition of "discrete". Unless you are thinking of discrete quantities and infinity as being one and the same at a deeper level of reality

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I'm left wondering how the concept of superposition is reconciled with conventional notions of logic in philosophy. Also, does the standard notion of logic collapse if there is no clear reconciliation (i.e. are we then forced to admit to the fallibility of conventional logic)?

This is not just a problem of conventional logic, it's more like a deep epistemological abyss, as conveyed by the inability of physicists to understand what things(objects) are. It could either be a limit to knowledge or a deeply rooted misunderstanding that we carried on through the centuries.

Fringle patterns to infinity are not consistent with Oxford's definition of "discrete".
1. Have you ever seen any pattern extending to infinity?
2. Even if so - where is inconsistency?
Natural numbers extend to infinity and they are "discrete" if you look at them with real numbers in a background.
Of course, infinite pattern must be composed of infinite number of "discrete" elements, the same way as finite pattern is composed of finite number of discrete photons.
But "infinite number of distinct elements" is not an oxymoron.

1. Have you ever seen any pattern extending to infinity?

I don't have to. You have never seen an electron, yet you can measure and deduce its properties. The probability amplitude peaks at a definite point in space and becomes zero everywhere else only after a measurement is done. This has been experimentally verified and implemented in a number of applications.

2. Even if so - where is inconsistency?
Natural numbers extend to infinity and they are "discrete" if you look at them with real numbers in a background.

There is clearly the contradiction that LostConjugate spoke about - it's a problem of classical realism and lots of human baggage. But to say that there is no contradiction with our everyday concepts when an electron interferes with itself, is an exaggeration.

Of course, infinite pattern must be composed of infinite number of "discrete" elements, the same way as finite pattern is composed of finite number of discrete photons.
But "infinite number of distinct elements" is not an oxymoron.

Thinking of an electron in motion towards the detector plate as an "infinite pattern" and then interfering with itself gives everyone a headache. If you think you understand how a single electron can pass through both slits at the same time, that's a solid indication that you don't understand it.

But to say that there is no contradiction with our everyday concepts when an electron interferes with itself, is an exaggeration.
Really? Isn't all that contradiction contained in intuition baggage depicting an electron as an electrically charged snooker ball?
If you think you understand how a single electron can pass through both slits at the same time, that's a solid indication that you don't understand it.
I just don't think about "single electrons passing through anything".
I think about electron existence only at the very beginning (as it is emitted) and at the very end - as it is detected. So it is not electron, which interferes with itself, but wave function. Wave function or whatever else you like to use in calculations - are artificial concepts, useful to predict experimental results. Like a "gravity force" is an artificial concept helping to predict Moon eclipses.

Really? Isn't all that contradiction contained in intuition baggage depicting an electron as an electrically charged snooker ball?

Most certainly.

I just don't think about "single electrons passing through anything".
I think about electron existence only at the very beginning (as it is emitted) and at the very end - as it is detected. So it is not electron, which interferes with itself, but wave function. Wave function or whatever else you like to use in calculations - are artificial concepts, useful to predict experimental results. Like a "gravity force" is an artificial concept helping to predict Moon eclipses.

This works for removing contradictions, but if we can't understand what matter is, we are in no better position to know the world than we were in the Stone Age.
It seems to me that most physicists have now tacitly accepted that reality happens(essentially giving up realism) as opposed to reality exists, without going deeper what it all means(or they simply don't like the implications or are too shallow to follow the ramifications through till the end).

Indeterminacy is at the heart of superposition and what Indeterminacy does is challenge the law of identity. More recent evidence that even entanglement is subject to Indeterminacy again places the focus squarely on the law of identity suggesting that either our definitions of quanta require revision, the law of identity requires revision, or both. Which it might be is anyone's guess at this point.

I'd compare it to the discovery of the constancy of the speed of light which seemed to defy conventional logic and the known laws of physics. At the time nobody knew if logic required revision, the laws of physics, and or their definitions. We could speculate endlessly, but there is no clear evidence yet that supports any one view.

There is clearly the contradiction that LostConjugate spoke about - it's a problem of classical realism and lots of human baggage. But to say that there is no contradiction with our everyday concepts when an electron interferes with itself, is an exaggeration.

Thinking of an electron in motion towards the detector plate as an "infinite pattern" and then interfering with itself gives everyone a headache. If you think you understand how a single electron can pass through both slits at the same time, that's a solid indication that you don't understand it.

It is not impossible to imagine that we extend QM with various unnecessary ideas and concepts and thereby achieves a local 'realistic' description of the double-slit problem.

First postulate: the space is not empty - with dark matter and dark energy it is not so unlikely - but then we have the ether back.

Second postulate: particles creates waves in the ether corresponding to QM's descriptions.

These waves create possible interference.

These wave guides the particle.

I think De Broglie thought something like that - But Bohm build a deterministic theory upstairs?

Most physicists would say that these decisions are ugly and unnecessary when they do not make any measurable difference.

It is not impossible to imagine that we extend QM with various unnecessary ideas and concepts and thereby achieves a local 'realistic' description of the double-slit problem.

Local realism lives in the classical world, and usually it's a shock the first time people hear of there being no classical substance in this reality at all. It's an incomprehenisble quantum "substance" that strains towards classicality via processes like decoherence, collapse, symmetry breaking, etc. Observed local realism is the end result of fields acting in a classical-like way.

First postulate: the space is not empty - with dark matter and dark energy it is not so unlikely - but then we have the ether back.

Second postulate: particles creates waves in the ether corresponding to QM's descriptions.

These waves create possible interference.

These wave guides the particle.

I think De Broglie thought something like that - But Bohm build a deterministic theory upstairs?

Most physicists would say that these decisions are ugly and unnecessary when they do not make any measurable difference.

Yes, they are the crutch on which realism as we know it, is supposed to hold. But I'd say that the BI adds more mystery than it removes. Classicality is deceptive, there's many a wrong path to take. No wonder physicists need an infinite number of worlds to explain ours(or rather explain it away).

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