Does Quantum Mechanics Invalidate the Law of Non-contradiction? Part 2

Post Author: Bill Pratt

In part 1 of this series, Walt Tucker gave an explanation of the two slit experiment and its relation to quantum mechanics.  In part 2, Walt explains why this experiment does not violate the law of non-contradiction.  Below are Walt’s words.

The quick answer is: if a particle could actually be observed as A and not A at the same time, that would violate the law of non-contradiction. Since that cannot be done, even in the quantum world, there is no violation!

Quantum superposition is the mathematical addition of probability densities of all of the possible states of a quantum system.  The result of the superposition of the densities is used to calculate the probability of observing the system in one of the states.  In a binary probability space there is a chance that a quantum event can be observed as A or as not A.  

In the two slit experiment, it is the probability of a photon going through slit A or slit B.  Slit B would be not A.  When you don’t observe the slits to know which slit the particle went through, you find that it goes through both.  So, this guy is saying that both A and not A exist simultaneously and the law of non-contradiction is violated.  But that is not exactly the case!

When the quantum system is observed, it is observed in the context of a particle with specific location and it can only be A or not A, it can’t be both. But when the system is not being observed, it is not in the form of a point like particle, it is in a wave form where the quanta of energy is spread across the possible states as a wave.  It is in the wave form until it is observed. The observation collapses the wave to a point like particle where the law of non-contradiction is also observed (like popping a whole balloon by a pin at only one point on the surface of the balloon).

One could say the law of non-contradiction is only valid in the world of observables (the world in which we interact). But it can also be said that since the energy is in a wave form when it is not being observed, that it is not true that it is A and not A at the same time, but that it is something else, a wave, that only has the potential to be either A or not A once it is observed.  In other words, it is a whole other form that makes no sense in terms of A and non-A.

It is like saying a potato is mashed potatoes, French fries, and a baked potato all at the same time, when it is not any of them when it is a potato in the garden.  The potato has the potential to be any of those forms of potato, but isn’t any of them until one takes the potato and does something with it.  The same thing applies in the quantum world.  A wave has the potential to be observed at slit A or slit B (since a quanta of energy must be observed at one point), but while it is still a wave, it cannot be observed at both slits at the same time because an observation would cause it to no longer be a wave, but a particle.

Bottom line is that having the potential to be one thing or another does not violate the law of non-contradiction.  If the particle could actually be observed as A and not A at the same time, then there would be a violation of the law of non-contradiction!

[Bill Pratt]  Thanks for the explanation, Walt.  Great stuff.

  • I provide the attached image to help people see how individual photon events accumulate to what we see in the regular world. The interference pattern isn’t obvious when observing a small number of photons.

  • Loretta

    How you choose to observe something changes your understanding, not the object itself. The difference in findings based on the method of observation indicates a lack of a complete understanding of the particles. What it really means is that there is simply more to know.

  • Todd


    What are your thoughts on this article which begins:

    “A team of scientists has succeeded in putting an object large enough to be visible to the naked eye into a mixed quantum state of moving and not moving.”

  • Todd,

    First, from the article, “Through a phenomenon known as ‘superposition’ a particle can be moving and stationary at the same time–at least until an outside force acts on it. Then it instantly chooses one of the two contradictory positions.”

    You have to be careful with the words used in articles like these. They tend to want to hype things. The statement above from the article says what I said but with imprecise language to make the experiment sound more mysterious than it really is. When an object is in a superposition state (wave mode), it’s energy is spread out into all of the possible states. Nothing is contradictory unless all of the energy was observed in one state and the other simultaneously. From this article it may sound like the object is in two contradictory observable states simultaneously, but an observation of contradictory states requires transfer of energy from the object to a detector which can only happen in a single state in the quantum world (because of the quanta nature of energy). Once the transfer happens, the original object no longer exists as its own entity (it has been absorbed). The outside force mentioned above is the detection mechanism which causes the “spread” to collapse to one specific state.

    The device in this article is “vibrating.” They use words like “moving” and “not-moving.” When we think of something as moving and not-moving, we think of that as contradictory because we expect actual motion from point 1 to point 2. To say something is moving from point 1 to point 2 and not moving from point 1 to point 2 would indeed by a contradiction. However, that is not what is happening with this device. Notice they call it a “drum.” I happen to play drums. Ask a drummer sometime whether he/she ever sees the head of the drum vibrate in several frequencies simultaneously? What the drummer sees is a superposition of frequency modes. There is no contradiction there. The energy in the drum head is split between several frequencies. Frequencies are not contradictory states. In this experiment, the lowest frequency is zero – stationary. And then there is a pure vibrational frequency. While there is a visual observation of the drum, there is no transfer of energy from the drum to a detector in the same sense as detecting a photon at a detector in the two slit experiment, thus the superposition is not destroyed.

    If anything, this experiment verifies that the quantum circuit the device was attached to is indeed in a superpositional, wave like mode until something causes the quantum state to collapse (be absorbed and stop operating). Once that happens in this experiment, the drum begins to either vibrate with the pure frequency, or not vibrate. The drum itself is not the quantum entity, the circuit it is connected to is.

    Hopefully that was clear. Bottom line is that there is a lot of hype in the science world in order to sell magazines.

  • Todd


    Thanks for the long, but clear reply. I am by no means an expert on QM, but find it fascinating. In reading the article, I found the sentence on ‘superposition’ to seem askew to what they imply with the title paragraph though I didn’t have enough understanding of the subject to grasp its meaning. It is always more difficult to discern the truth when it is portrayed with the thick accent of marketing.

    I intend to write the author and see if I can get him to clarify his seemingly profound statements!

  • Todd, I’d be interested in seeing what they say. I saw a talk once by a guy associated with a group from Harvard that slowed light to a stand still. They continued to use words as such, but when you looked at what they were really doing, they were holding the phase still, but the light that made up the pulse was still traveling at the speed of light. In a sense (but not exactly the same) that would be like watching a water wave while traveling at the speed of the wave. It would “look” like it was standing still.
    So, it would be good to hear what the author says outside of writing a magazine article, but he might use verbage that is not quite accurate.

  • Boz

    Apparently, according to the Franson experiment, we can release one photon into an experimental apparatus at a particular point in time, but the experiment shows us that the individual photon must have been released at two different times.

  • Boz,

    The important part is, “There’s some subtlety that I’m not including, such as the fact that
    paths above are only half of the device (the other half is identical),
    and that the experiment requires entangled photons.” That subtlety is the reason the experiment works the way it does. It is impossible to get the result outlined in the link without considering the entire experiment. The problem is that the author of this blog is describing the experiment entirely as a particle problem. That’s what I said in the previous discussions here that you can’t do since there is not really a “particle” until detection. In the real experiment there are 4 detectors (two pairs, where each pair is treated as one). The interference effect appears because the “wave” is travelling all possible paths at the same time. With only one side of the experiment (the part described in the blog) you get a “ping” of the detectors randomly at effectively either the short path or the long path and there is no interference between the paths since the path length difference is too large. The “wave” took both paths, but the detectors can only detect the energy of the photon at one detector or the other for any one event (the same as having detectors at the two slits of a two slit experiment).

    But, when we consider both sides of the experiment and that there are two coupled (entangled) photons, there is an interference between the paths on the right side and the paths on the left side. They never spatially interfere, but time interfere such that they ping the detectors at the same time or not. The path lengths can be adjusted (or a phase plate used) that construct an interference pattern such that either the short paths or the long paths are taken together by the two photons on both sides (which path was actually taken is random, but which ever one is taken is taken on both sides in the same way) or the opposites are taken. That the opposites can be taken gives the appearance that the two photons were emitted from the source at different times (destructive interference case). However, this is not the case. Rather, the net interference gives that effect.

    My interpretation of this comes from the math in the paper that was referenced. By the way, the experiment in the Physical Review Letters was theoretical and not an actual experiment. The author of that paper, Franson, stated the experiment would be difficult to do because of instabilities.

  • machinephilosophy

    If the law of noncontradiction were violated, uncertain, restricted, etc., it’s difficult to see how one could know that fact itself. The problem is that any negation or diminishing of the law of noncontradiction is itself logically dependent on that same law in order to have a meaning distinct from that law’s affirmation, certainty, invariance, and so on. Any qualification to mere suspension, uncertainty, etc. merely shifts the problem to the new qualification, and necessarily repeats the arbitrary self-referential exemption.

    Concerning logic and the existence of God, the most basic set of criteria is always already God-level. And since such criteria is universal, and therefore applies to everything including the nature of personhood, such ultimate criteria implies the existence of God. Otherwise, you’re just arbitrarily treating the background set of necessary assumptions and rules of thought as an invisible cognitive friend.

    The above is of course highly enthymemic. This “atheistic criteria” argument is based partly on atheist Kai Nielsen’s argument for the necessity of an independent moral criterion on page 31 of his Ethics Without God (2nd edition, 1990) but generalized to include the most general level of criteria. See my, the second post down, for the complete argument.

  • Sapient1

    Thanks Walt
    I have run across the same argument…

    …always seems a bit odd how someone can leap from this, quantum mechanics phenomena, to a justification of some form of immorality.

    God bless

  • MariusDejess

    What is the difference between a wave and a wave function?

    And what is the difference between a wave and a particle?

    As I understand things, wave and particle are things outside our mind, but a wave function is a concept in mathematics.

    Please correct me.

  • Jay M.

    Good article. Thanks for the explanation. However, you close with “If the particle could actually be observed as A and not A at the same time, then there would be a violation of the law of non-contradiction!”

    An experiment in Nov 2012, seems to have done exactly that (or at least, that is what is being claimed of it).

    “The measurement apparatus detected strong nonlocality, which certified that the photon behaved simultaneously as a wave and a particle in our experiment,” physicist Alberto Peruzzo of England’s University of Bristol said in a statement. “This represents a strong refutation of models in which the photon is either a wave or a particle.””

    What do you make of that? Does it indeed, pose a challenge to the 1st principle? Or is there something in this experiment that Peruzzo is misstating as a consequence of it?.

  • Jay, I’m looking over the article as reported in Science and will get back to you. In the explanation above, the entity is a wave until detected. You never ever actually detect a wave – it is a matter of whether the particle (the net detection) exhibits the interference pattern over many detections or not (two slit with no detectors at the slits – wave nature at the slits is still intact; versus two slits with detectors at the slits, which destroy the wave nature at the slits). Thus, I doubt that the law of non-controdiction is being violated in the delayed experiment, since an entity is a wave until detected and it is only the form of the setup that determines whether there is an interference pattern or not, even if the selection of the appartus is delayed.. But, to be able to explain properly what is going on, I need to review the article.

  • Marius Dejess, a wave function is a mathematical expression that is used to determine the probability of an entity being observed in a particular state. Thus you are correct on that matter. A wave can exhibit an interference between possible states observed over multiple quantum detections indicating that the possible states exist simultaneously until detected.. A particle, as often defined in QM, does not exhibit interference and has only one state or another (the wave interference effect already destroyed). In the explanation above, a particle is merely the detection point of a collapsed or interacting wave. So, it is better to say there is no such thing as a particle except as a detection of a collapsed wave. The wave function then allows one to determine the probability of a detection of a state as the wave collapses, or at least interacts with a detector. Depending on the experimental setup, the detection reveals the interference pattern or not (whether it is a wave or particle in QM lingo).

    Since a quantum entity is a physical thing, it indeed is outside the mind. Yet, some try to say there is a link. I do not subscribe to such a link other than that a person’s physical presence makes up part of the stochastic environment which influences the outcome of an experiment. The behavior of the experiement is the same whether there is an actual observer or not. Intelligence only plays into the outcome by the fact that an observer, who sets up the experiment, should have some, and is usually involved in the actual observation. There is nothing mystical about it. So again, you are correct.

    Thus, given you are correct on both matters, what is the point you are trying to make?

  • Jay, I looked over the article. First let me clairify something about my statement of a particle being observed as A and not A would violate the law of non-contradiction and what is going on in this experiement. Observing the particle at slit 1 (A) and at slit 2 (not A) as particles simultaneoulsy would indeed be a contradiction. The particle cannot be observed at both places simultaneously. This is fundamental to quantum mechanics regardless of the interpretation. The experiment in the article is not about observing a particle going through both paths simultaneously (the equivalent of observing a particle at both slits in a 2 slit experiment – ie. when the system in the article is in the state of effectively have the 2nd beam splitter of the interferometer), but about determining whether the “decision” of whether the wave nature or the particle nature of the quantum entity exists prior to the measurement in a hidden variable. It is a fact of any interpretation of QM that the apparatus determines the nature of the measurement. When a detection of the paths (which slit, or which path of interferometer) is made, the photon acts as a particle. When the detection method does not “watch” the paths (slits), the interference effect of the wave nature is observed.

    The exeriment verified that there is no hidden variable and the “particle” or “wave” nature is not determined ahead of time. I entirely agree with this! What I disagree with is the copenhagen interpretation that assumes that a quantum entity exhibits the wave and particle nature simultaneously. The experimentalist assume that both natures exist until observation. My point in the explanation above is that the entity is a wave until detected. Since it is detected at a point, giving the appearance of a collapse of the wave to a point, the particle nature is in effect the result of the detection process itself. Since the detection method is determined by the experimental setup, whether you observe an interference effect or not is determined by the setup. That you delay the observation makes no difference since the effect is not observed until detection.

    In the Wheeler experiement, the photon splits at the first beam splitter, as a wave, and if the second splitter is left in place, there is an interference that cancel any detection on one of the two detectors. Thuse always detecting the photons on one detector is the verification of the wave nature. Yet, if the second splitter is removed after the photon splits, you detect the photon equally on either detector which shows there was no interference and the quantum entity acted like a particle going one path of the other. In my explanation above, the wave has interference properties and detection can only happen where there is enough intensity of the wave to excite an electron in the detectors. When the interferometer is closed, the intensity of the wave is zero on one detector and one on the other. This is called out as probabilities in QM calculations. Yet, when the second splitter is removed, there is no interference pattern of the photon on the detectors (because no physical way was provided to produce an interference – mixing of two paths of the wave), and thus there is equal intensity of the wave on both detectors and in probability terms equal probability of detecting as either detector. In my explanation, the probability lies in the detectors, not the entity itself. The intensity of the entity wave function at the detectors gives a relative strength which results in a probability of exciting the detector.

    In the case of the experiment of the article, which is an adaptation of the Wheeler experiement, a superposition is set up of mutliple detection schemes and that superposition effects the intensity of the net wave function, and thus probabilties at the detectors. They aren’t simultaneously observing a particle and a wave, but simulteously observing an interference pattern and a non-interference pattern. These are not contradictions, but superpositions of the wave nature that exists in both detection schemes. So, it is not that there is a wave and a particle, but that the apparatus is mixing detection schemes.

    If anything, this experiment further validates the wave nature of quantum entities and the particle like effect of detection. Delaying has no effect since the nature of the path is not resolved until detection.

    This is not the easiest thing to just jot down in a blog without taking a lot of time to figure out the best way to explain. But I hope this has made some sense and that you can see that no violation of the law of non-contradiction has yet occured. Again the quantum entity is in many potentialities until it is actualized at detection.

  • By the way, my long explanation just posted is to say that Peruzzo is confusing things a bit because of his use of the copenhagen interpretation. Nothing he and his team have done shows that an entity is simultaeously a wave and a particle. Rather he has shown that you can create a device that gives the effect of both at a detector pair. It is easist to just think of a quantum entity as an actual wave consisting of a superposition of all of the possible states that collapses to a point (particle) when detected.

  • David Kempton

    What actually produces the interference pattern when you do the double slit experiment with particles? Is the particle some sort of particle-wave thing that is disturbed by the device used to detect it?

    Also, what would happen if you put a detect on only one slit when doing the experiment?

  • David, Best to think of the entity as a wave of a quanta of energy that passes through both slits (a particle-wave thing, as you said). Because the wave is coherent, with well defined wave fronts, an interference pattern forms after the slits in the manner described in books on diffraction of lght. That pattern presents an effective field strength that varies across the detector (film). Since the wave is an indivisible quanta, the entire wave must collapse at a single interaction point. The probability of interacting at any point in the film depends on the strength of the wave across all those points. So, the probability aspect comes into play, not because of the probability of a particle being in a particular location, but because of the probability of any one electron in the detection device to capture the energy based on field strength of the wave. The particle aspect comes into play because of the quantum nature of the wave as a whole (it all collapses together). The wave aspect comes into play because it is a wave with an intensity pattern. So, to answer your first question, it is indeed a particle-wave thing that is disturbed by the device used to detect it. When detecting just a few photons, you only see dots on the film. When a large number of photons are detected, the interferrence pattern starts to be noticeable. See images in the first posting above after the article.

    So, when a detector is put at one of the slits, the first collapse of the wave occurs there instead of at the film on the othe side of the slits. You can think of it as a new wave then emerges from the point in the slit where it was captured. Since it now emerges from a single point, there is no interference pattern. Without the interference pattern, the field strength at the film behind the slits is interference free and the probability of interaction with any electron in the film is spread more evently across the film.

    This interpretation of the quantum phenomenon is much more intuitive, matches what the mathematics practically verbatum, and gives the proper results while not violating anything we understand at the macroscopic level. It isn’t necessary that the wave truly collapse, but the effect of an interaction is the same. The main thing is that the probability is in the detection process based on the field strength of the entity, not on the probability of individual particles to be in a particle location.

  • David Kempton

    Very interesting theory.
    Does it imply that all matter is made up of waves?

  • David, that would be an implication, but might be better to say that it is the underlying assumption, i.e. what went into the interpreation rather than what came out of it. What comes out of it is an explanation of quantum mechanics that is consistent across all scales of observation. The oddity of it still is the idea that the waves are a quanta of energy that cannot be divisible. To support the interpretation: Matter waves have been detected. Superposition of states have been observed. If they are real things, then why treat them as only mathematical constructs of particles with uncertain position and momentum? As well, this interpretation does not violate any principles of logic such as the law of contradiction or the law of cause and effect.

  • Curious, I clicked on your name and saw the video you posted. I didn’t have time to watch the whole video, but went to the end to get the gist of what the speaker was saying. I would not call this an illusion. There are real interactions going on. There is real information involved. Granted it looks different down at the quantum level than when it all builds up to the macroscopic level. but it is very real! I think some people like to use certain words to bring mystery to the discussion. For example, there was a lot of hype out of Harvard not too long ago about some experiement to stop light. You can’t stop light! What they stopped was the phase velocity of the light (the observable part or that part which results in interference being possible). But, saying they stopped light sells magazines and gets you in the newspapers. That this speaker says bits of information as not real, is his computer science background at play. A simulation is a real thing (an operating computer program) that models something else. But his term of simulation is an analogy to help understand things. Since reality is reality, I wouldn’t call it a simulation. Even if we thought of reality as the product of God’s mind, it is a real product with real actors with real pain and suffering that needs to be addressed by freewill agents responding to that God.

  • David Kempton

    Do you agree with Bill’s response to my comment where he basically said:
    Quantum mechanics cannot be used to prove the universe is an illusion, or indeed a simulation, as since quantum mechanics operates in the universe it is also part of the illusion or simulation; therefore we can discount any such theories?

  • I think that speaker means illusion in a different sense. But, if it is said what we observe is an illusion, in that it is not what is true, then it is obvious that we can’t even trust what we think is the source of the illusion, because it is part of the world of the illusion. For illusion in that sense, I agree with Bill. (I didn’t see Bill’s response.) However, I don’t think the speaker means illusion in that sense, and his use of simulation is an analogy, from what I gathered. Thus, his terms add confusion to the whole talk and don’t adequately convey what he was teaching. His idea of illusion is that what we think we see isn’t really what we see, but is the effect of what we really see. If it is the effect, then it is still what we see, i.e, the effect is real, and it is us seeing it. We are not buried within a Matrix type of thing. I can’t prove we are not in a Matrix, but there is nothing in the theory which says we are, no matter what words someone wants to use to describe it. That what happens fundamentally is like how a simulation works does not make what is going on a simulation. If what is going on is not real, then we would not be here to talk about it.

  • David Kempton

    This is all a bit deep for me. But basically, if the speaker’s theory is true, it still wouldn’t support any sort of spiritualist/new age nonsense or invalidate any of the evidences for the Bible?

    Also, I’m not sure if you listened to this part but he talked about how measurement and entanglement are the same phenomenon. What are your thoughts on that?

  • Some will try to use it to support new age thought, but it doesn’t. If you understand the way I described it as wave phemenon of energy packets, it is not so mysterious and does not require some sort of consciousness to work. In no way does it invalidate the Bible.

    I would agree that measurement and entanglement are the same thing. I did not watch all the details of that portion of the talk, so there could be a nuance in there that he said that I might not agree with. But, in my wave description, even though I use the words “collapse”, I also said it doesn’t require actual collapse. The alternative to an actual collapse is an entanglement type of mechanism. I think most theorists today are leaning towards the entanglement view. His information ideas can be implemented by pure waves and the “particle” nature comes from the “detection” which is the effect of the entanglement. Mathematically, it all looks the same.

  • David Kempton

    I think I might just try to forget about the whole thing as it’s ruined my life, I can think about nothing else. There are so many disturbing theories going around in my head, I feel like my mind has been poisoned for good. I regret that I ever got interested in this quantum theory.

    Thanks for all the replies anyway.

    God bless.