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Byron Jennings | TRIUMF | Canada

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The Interpretation of Quantum Mechanics

When I first started dabbling in the dark side and told people I was working on the philosophy of science, the most common response from my colleagues was: Oh the foundations of quantum mechanics? Actually not. For the most part, I find the foundations of quantum mechanics rather boring. Perhaps that is because my view of science has a strong instrumentalist tinge, but the foundations of quantum mechanics have always seemed to me to be trying to fit a quantum reality into a classical framework; the proverbial triangular peg in an hexagonal hole. Take wave-particle duality for example. Wave and particles are classical idealizations. The classical point particle does not exist, even within the context of classical mechanics. It should come as no surprise that when the classical framework breaks down, the concepts from classical mechanics are no longer valid. What quantum mechanics is telling us is only that the classical concepts of waves and particles are no longer valid. Interesting, but nothing to get excited about.

The problem with the uncertainty principle is similar. This principle states that we cannot simultaneously measure the position and motion of a particle. Now, classically, the state of a particle is given by its location and motion (i.e. it’s momentum). Quantum mechanically, the state is given by the wave function or, if you prefer, by a distribution in the location-motion space[1]. Now the problem is not that the location and motion cannot be measured simultaneously but that the particle does not simultaneous have a well-defined position and motion since its state is given by a distribution. This causes realists, at least classical realists, to have fits. In quantum mechanics, the position is only known when it is directly measured, ie properties of the system only exist when they are being looked at. This is a distinctly antirealist point of view. Again, this is trying to force a classical framework on a quantum system. If anything is real in quantum systems, it is wave functions, not individual observables. But see below.

Quantum mechanics is definitely weird; it goes against our common sense, our intuition. The main problem is that, while classical mechanics is deterministic, quantum mechanics is probabilistic. To see why this is a problem, consider the classical-probability problem of rolling a dice. I roll a fair dice. The chance of it being 2 is 1/6; similarly for any value from 1 to 6. Now once I look at the dice the probability distribution collapses. Let’s say, I see a 2. The probability is now 1 that the value is 2 and zero for the other values. But for Alice who has not seen me check, the probabilities are still all 1/6. I now tell her that the number is even. This collapse her probability distribution so that it is 1/3 for 2,4,6 and zero for 1,3,5. Now for Bob, who did not hear me telling Alice, the probabilities are still 1/6 for each of the numbers. Two important points arise from this. First, classical probabilities change discontinuously when measurements are made and, second, classical probabilities depend not just on the system but on the observer, ie probabilities are observer dependant.

We should expect the same quantum mechanically. We should expect measurements to discontinuously change the probability distribution and the probability distribution to be observer dependent. The first is certainly true. Quantum mechanical measurements cause the wave function to collapse and consequently the probability distribution[2] also collapses. The second is not commonly realized or accepted, but it should be. The idea that the wave function is a property of the quantum system plus observer, not the quantum system in isolation, is not new. Indeed, it is a variant of the original Copenhagen interpretation of quantum mechanics. But frequently, it is denied. When this is done, one is usually forced to the conclusion that the mind or consciousness plays a large and mysterious role in the measurement process. Making the wave function, or the state description, observer dependent avoids this problem.  The wave function is then just the information the observer has about the quantum system. As Niels Bohr (1885 – 1962), one of the founders of quantum mechanics, said: It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.

Let us consider the wave function collapse in more detail. Consider an entanglement experiment. The idea is to have a system emit two particles such that if we know the properties of one, the properties of the other are also known. One of the two emitted particles is measured by Bob and the other by Alice.[3] Now, Alice is lazy so she has her particle transported to her home laboratory. She also knows that once Bob has done his measurement, she does not have to measure her particle but only has to call Bob to get the answer. Bob is also lazy, but he does go the lab and, if he feels like it, does the measurement and faithfully records it in his log book. One day when Alice calls, she gets no answer. It turns out Bob has died between the time he would have made the measurement and when he would have recorded it in his lab book. Now Alice is very upset. Not that Bob has died—she never liked him anyway—but that she does not know if the momentous event of the wave function collapse has happened or not. Her particle has not arrived at her home yet, but there is no experiment she can do on it to determine if the wave function has collapsed or not. The universe may have split into many worlds but she can never know! Of course, if the wave function is a property of the observer-quantum system, there is no problem.  The information Bob had on the wave function was lost when Bob died and Alice’s wave function is as it always was. Nothing to see here, move along.

So what is the interpretation of quantum mechanics? An important part seems to be that wave functions are the information the observer has on the quantum system, and is not a property of the quantum system alone. If you do not like that, well there is always instrumentalism,[4] i.e. shut up and calculate.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod.


[1] Technically, the phase space.

[2] The probability is the absolute value of the wave function squared.

[3] By convention it has to be Bob and Alice. I believe this is a quantum effect.

[4] Instrumentalism has no problem with quantum mechanics or, indeed, any other scientific model.

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16 Responses to “The Interpretation of Quantum Mechanics”

  1. Kea says:

    This post is OK, but an anti-realist stance cannot be so easily dismissed, since the world is indeed quantum. The problem with wavefunctions is that they are merely mathematical devices, not really physically descriptive. They may well be replaced with modern mathematical alternatives. Moreover, when we accept the presence of observers, as indeed we must, we see that their classical world of measurement events (the only Real Things, to an observer) must be distinguished from an a priori classical world, which clearly cannot exist in a true anti-realist framework. This is the problem with extending the wavefunction far beyond its domain of validity, onto ‘The Universe’ itself. If every observer has ‘A Universe’, we are then free to meddle with its properties without being constrained by the imagined, emergent classical world. In other words, let us forget those stupid, ontologically ugly Multiverses of constrained approaches to QG!

  2. gunn says:

    But it is proved (http://arxiv.org/abs/1002.3425) that the equations of the quantum theory describe not behavior of a particle but behavior of probabilities of the dot events occurring to this particle. Therefore, wave function is a characteristic of such probability, and it disappears together with this probability after event will occur, In double-slit experiment through both slits the wave of probability of dot event, instead of a particle flies by. And so on. Hence, here there is no quantum dualism between a wave and a particle, here is no collapse of wave function, here is no border between the macro-world and the micro-world, etc.

  3. JC says:

    Can you be more explicit about the definition of an observer? Sentient acknowledgement of a measurement is only a subset of what qualifies as an observer. The full realm of QM interactions with the system in question have the same “observational” manifestation.

    The word observation – without rigorous definition – is often misinterpreted to be a “human-in-the-loop”. Not true.

    • Byron says:

      In the end rigorous definitions are a mirage. Defining words in terms of other words has to ultimately fail. Rather the meaning of words must be sufficiently clear to allow communications. In many ways I am the observer and allow other people,or perhaps even things, to be observers by proxy.

    • JC says:

      Byron, I appreciate your prompt response but it sidesteps the issue. I think a mathematician would strenuously disagree with your comment that “rigorous definitions are a mirage”. Rigorous definitions of the terms we use to communicate and capture thought is necessary to avoid misunderstandings and frankly prevents sloppy thinking. Your second sentence still illustrates the ambiguity. A human “in-the-loop” to consciously recognize the result of a measurement is sufficient but not necessary to effect a system in a certain way. The effect a human “observation” has on a quantum system is no different than what naturally happens between similarly interacting systems in isolation. The universe behaves the same whether a human is in the loop or not.

    • Byron says:

      Unfortunately we are not doing mathematics but even in mathematics I suspect the problems with its foundations is related to the failure of rigorous definition. Rigorous definitions tend to spiral into oblivion: what it red – a certain combination of wave lengths, What are wave lengths? etc.

      Words meanings must be sufficiently understood for communications. For the present purpose we can take observer to be a person who observes.

      The universe evolves independent of me but what I know depends on me. There is one strain in the interpretation of quantum mechanics that claims consciousness plays a central role in quantum measurements. I heard this expounded by no less than Sir Rudolf Peierls. It seems to me the only way around this is to make the wave function observer dependent. It is only defined in relation to an observer.

  4. looka says:

    In last paragraph you make it sound like observer just doesn’t have all the information (as Bob and Alice with the dice) while mantra goes that information (or particle) fundamentally cannot be known.

    Uncertainty for position and momentum really works for classical waves just as well, so I agree with that, as well as the fact that quantum world is nothing we have seen in real world (waves and particles just being bad analogies), but accepting that it could never be visualised or better understood is just too much for me. I know Bohr won, but I’m siding with Einstein.

    • Byron says:

      Interesting comment. The real problem is that even when we know as much about the system as possible we still cannot predict individual events. I like your last sentance

  5. Tom says:

    I think that there is a problem with your analogy and subsequent conclusion that quantum probabilities, and their philosophical implications, are somehow to be expected as an outcome of equations that describe the particle-observer system.

    The probability distributions for dice rolls are purely statements about the observer’s knowledge of the state of the die. When that wave function collapses, there is no change in the physical state of the die. In quantum mechanics, the double-slit experiments an quantum entanglement experiments seem to show that the probability distribution is also an inherent property of the quantum particle (excluding the possibility of relativity violations).

    An analogy with dice would, I think, need to have the property that a die comes up both even and odd until it is observed, even long after it has stopped rolling. Only when it is observed does it take on a specific value. This is not merely a statement about the observer’s knowledge of the die, but one about the properties of the die itself.

    This is demonstrated mathematically by the Bell inequality, which has been experimentally verified, most famously by Aspect’s team in the early 80’s. Recent experimental work by Steinberg’s team might shed some new light on this.

    Where it gets really difficult, from a philosophical perspective, is that the observer is not defined. Experimentally we know that humans count as observers, though perhaps nothing else does, and hence we have poor Schrödinger’s cat.

    I look forward to future installments in this series.

    • Byron says:

      Classical we can assume without contradiction that the dice had the value before we looked at it. In quantum mechanics we cannot. It seems to me we get fewer problems with interpretations if we take the wave function to be observer dependent. However, I am happy to shut up and calculate.

  6. The weak point of qunatum mechanics is that it depends upon probabilities. Probability theory itself has never been proven, and yet we all accept its methods. What can you do with probabilities? It doesn’t give you much to work with. On the other hand Heaviside/Cauchy calculus can be applied to the real world to give exact and predictable results. We predict the future based on what has happened in the past. That, to me, is the essence of science.

    There is also a contradiction when it comes to wave theory, since waves are not mechanical entities. We need theories that envelope both the mechanical and electromagnetic properties of all phenomena. What is the size of an electron or a proton? Most every scientist will have a different answer to that question. Both are defined by their electromagnetic fields, and those fields do not have edges.

    Another problem with QM is the apparent dependence on a great number of equations to solve a problem. Max Planck was able to derive several of the laws of physics based mainly on just two basic equations. Where have you ever seen that before? Planck’s theory was indeed based on probability theory, and necessarily so. However, his theory applied to the actions of electrons and protons having various fixed energy states. These states govern the actions of the electrons moving in random patterns, similar to that of a gas, as another great scientist, Ludwig Boltzmann pointed out. So sometimes we need to consider probability theory, but not if we can avoid it.

  7. Joel Rice says:

    Feynman did not put all that much emphasis on the uncertainty principle, though his approach includes it because of equivalence with Schrodinger. I don’t think it is all that weird – “particles” are actually oscillators, rather than point charge or point mass, and have a complex phase. So now discrete spectra make sense because orbits need to have N oscillations, and that fixes Maxwell’s problem with atoms. The examples he works out in “QED: strange theory of light and matter” show how the Principle of Least Time emerges as a nice approximation- provided the amplitudes line up. One might think it is more complicated than classical physics, but it makes more algebraic sense, in terms of adding and multiplying complex numbers. The first couple of times I read it, I thought he had to be popularizing but it finally dawned on me that he was distilling a minimum number of assumptions that are central to the whole enterprise. The trouble with that book is that the more physics one knows, the better it looks, but the less physics one knows the more unmotivated it seems.

  8. Patrice Ayme says:

    Sir: this is my third submission in four days. The preceding two did not appear yet. Did you hear about weak measurements in the double slit experiment? If you did, I would like to know why you did not mention them. I am sure your reason(s) are cogent, and would appreciate to know them

    One of the proponents of these weak measurements (Legget) is actually a physics Nobel Prize laureate, and huge progress has been claimed in 2011. Another proponent is the famous Aharanov (from the Bohm-Aharanov effect). It seems to me that we have now direct visual proof that a De Broglie-Bohm theory is more appropriate than Bohr’s nebulous vision. But I do not doubt that you have some refined objection.

  9. Francisco Jackson says:

    There is a simple, but fundamental detail. It is called the “scientifc method”.
    As a method, it consists of several items to proceed. One of them is experimental verification. The scientist should provide concrete statements on how to prove that a proposed theory will correctly describe observed data or predict certain phenomena. If that is so, the theory can be regarded as a scientific one. Otherwise, it is not a scientific theory. It is called “speculation”. The end.
    Now, there are only 2 possibilities: 1- people deliberately want to dismiss the scientific method altogether in order to promote their speculative endeavors as some kind of new “science”. 2- They do not know what the scientific method is.
    Either possibility is disturbing. Specially if they teach to the younger generation.
    http://9pillsonline.com/

    • Byron says:

      Point 2 is the problem. Verification is generally regarded as flawed. Many models in science that have been regarded as verified have subsequently been found to be flawed. Similarly proof has no place in science only mathematics.

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