The wave function is considered to be unreal for a number of reasons. The first reason is that it is complex valued. So we might then say wave functions are not real, but they are complex. However, there is a bit more than this. It has a lot to do with the nonlocality of quantum waves and states. This is a fundamental departure from classical physics.

The theorems of Bell on nonlocality and the contextuality theorem of Kochen-Specker and other related results are inescapable. Now of course this is the case in this entire world except for here at FQXi, where the blog site has succeeded in doing what Feynman told us to do if we did not like QM:

https://www.youtube.com/watch?v=_sAfUpGmnm4

Go somewhere else. So the FQXi blog site is a little bubble that we might say has escaped the universe --- or some have this delusion.

If you want to say that in some metaphysical sense the wave function is real then go ahead. I suppose most physicists at times do this any ways. It is just that this ontology is of a different nature than our standard idea of what reality or "ontic" means. The wave function is better thought of as epistemological, and it gives the set of probability amplitudes corresponding to measurement in qubits or quNits (a set with N amplitudes).

As Richard Feynman says, if you don't like this, go somewhere else.

LC

    If wave-functions are not real objects, admittedly with strange properties, then how does one interpret the nature of quantum mechanics. I believe Feynman told us not to try to interpret it, just keep calculating. Beyond Feynman's suggestion, there remains the MWI interpretation, which is too unruly by creating universes at the point of the eigenvalues and ushering them off to oblivion in some magical way.

    But the beauty of wave-functions is that, if they do exist, they are subtle, unpresuming, and easy to see. The infinite potential energy well generates a wave-function of something as simple as

    [math]\psi(x) = A_0 cos (\frac{n \pi x}(L))[/math]

    A college professor could point to that and say, "we think that is something that actually exists." Everyone would breath a sigh of relief that quantum mechanics actually matches the physical universe.

    There is with quantum mechanics what I call an incompressible fluid of confusion. The fluid can be squashed flat or drawn into a thin tube and so forth, but the volume remains the same. We have gotten very good at manipulating this blob of fluid, and in doing so we illuminate some things, but we do not know the answer to questions such as how eigenvalues obtain in measurements or how nonlocality results in a completely local outcome. This stuff is bizarre, and I frankly doubt we will ever understand answers to these questions. I think these questions are not answerable; they are not relevant questions. The confusion comes in part because we have these classical brains, brains that know the world in a classical sort of way, and we have trouble processing these things. These questions are unanswerable because we want classical answers to questions about something that can't possibly give such answers.

    The human brain has circuits meant to find order in things. People become compulsive gamblers because they get hooked on a mind trip of trying to figure the game out. When we listen to music our brains make order out of it, and when order is hard to find we feel uncomfortable. Remember that Stravinsky's "Rite of Spring" caused a riot in its 1913 premier in Paris, and people's brains were literally rebelling against this music they did not understand. We have in science similar rebellions. Of course the rebellion against evolution is still underway, even though this is 19th century science historically at about the same time as Maxwell's equations, and we have rebellions against quantum mechanics and there is an oddball on this blog who insists Einstein was all washed up.

    Attempting to find answers to these quantum questions is I think a bit like the compulsive gambler who thinks they will figure out how to beat the house. These things are not going to work, for quantum mechanics is not going to offer up the classical world view such ideas about "real wave functions" and hidden variable theories and the like are attempting. People will continue to do this, and it is a bit of a trend in line with people trying to build perpetual motion machines and the like. Wise is the person who knows when a challenge is an illusion and can not be beaten; the wise man knows the limits of the world and themselves. The fool pushes relentlessly onwards on their steed Rocinante.

    LC

    Re "This is the way nature works! - Richard Feynman" (https://www.youtube.com/watch?v=_sAfUpGmnm4 ):

    "I'm forcing upon you a lecture on the things that we think we know something about" (0:12)..."the students do not understand it either , and that's because the professor doesn't understand it" (1:40) ... "Nature is strange as it can be...the RULES...are so screwy you can't believe 'em! " (2:17) ... "if you don't like it, go somewhere else to another universe where the rules are simpler" (4:52) ... "nobody understands it" (6:27)

    Lawrence, I believe that you and others are too content with surface appearances. What is the physical reality behind these law-of-nature "rules" which generalize/represent individual physical outcomes? What is the physical reality behind the numbers we use to represent physical outcomes, including the unpredictable individual physical outcomes from quantum processes? What is the physical reality behind the necessity to use complex numbers and pi? Forget about complexity of "the wave function" - there are far more basic issues than that!

    Do you take law-of-nature rules and numbers for granted; do you take them as given inputs to the system; i.e. are you a platonist?

    Lorraine

    I know someone who was shoved down the stairs by an angry ghost. There is video evidence of people being scratched and bitten by ghosts. Now I don't know how to get a ghost to do tricks for the physics community. All I can tell you is that from the cozy perspective of a university physics department or a cushy job in a laboratory, you're probably not witnessing the physical activity of ghosts. If you're not witnessing their activity, then you might think it's all neurochemistry.

    But I'm must looking at ghosts from the point of view of: how much more physics would be necessary to support their existence? As near as I can tell, a ghost has to be able to generate a potential energy V(r,y) without using electrical charges. It would do so by manipulating virtual photons. If it could do that, then a wave-function would spring into existence that represents the V(r,t). That wave-function would have energy and momentum states available, and the ghost could use it to flash those evil red eyes, move stuff.

    I can't think of any reason why physicists would think that the laws of physics are complete. They are not complete. Therefore there is new physics that we haven't discovered. The only phenomena that scientists haven't really studied is the activity of ghosts. It's because ghosts are very subtle. But why shouldn't they be subtle? If wave-functions exist, then wave-functions are also subtle. But is there a better explanation of quantum mechanics other than the proposition that wave-functions are real things? Very subtle, real things.

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    jrc,

    Integrating over future data in case of an analysis of past data is not the only indication of obvious nonsense. The first reason for me to wonder was the astonishing superiority of spectral analysis within the human ear as compared with the so called spectrogram. We must not attribute this superiority just to brain. Physiology contradicts to the interpretation of cochlea in terms of Fourier analysis. A major problem of the latter is the choice of width and position of an appropriate window of time. Theory of signals relies to an event-related time scale with arbitrarily assumed zero that is definitely not known to the ear. The position of the window on this scale is just valid for one also arbitrarily chosen moment. This requires awkward permanent relocation of the window. Moreover, the spectrogram exhibits non-causality, and the one-way rectification of the hair cell response would be impossible in case of a complex cochlear analysis while it is physiologically evident.

    Why are experts reluctant to abandon complex models although cosine transformation has proven equivalent in practice of coding? They are not ready to question the necessity of Fourier analysis in the theory of signal processing, ict, and ih in quantum theory. Don't get me wrong. I still enjoy using complex calculus as a tool but not as a gospel. A drunk person may consider himself and her mirror picture as two persons.

    Eckard Blumschein

    I am not commenting on ghosts; I think that definitely gets into supernaturalism.

    We have no clear understanding of the relationship between physics and mathematics. There are some people who claim that mathematics is physics, but I fail to see how this can either be proven mathematically or demonstrated experimentally. If you think that mathematics precedes physics there is then a sort of mysteriousness of how pure mathematical structures become reified. If you think that physics precedes mathematics then one is left with the unknowable "stuff" which composes reality. Asking what is the relationship between mathematics and physics heaps another unknown or unknowable onto the picture.

    I think the most reasonable way of thinking about how quantum outcomes of measurements occur is to think of consciousness as a sort of illusion. Consciousness is probably some form of epiphenomenon, similar to virtual images in optics, that occurs with neural activity. The occurrence of a quantum outcome is then a sort of illusion generated by this illusion. In that way we have an illusion of being taken along one particular MWI world branch or eigen-branching of the world.

    I don't have time to go into this, but I think this is connected to our perception of another illusion called time.

    LC

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      Eckard

      "cosine transformation has proven equivalent in practice of coding"

      I think both Peter Jackson and Robert McEachern are in general agreement with you as to Fourier Analysis, though with their own qualifications from different perspectives. The question as to Why Quantum? is still open. I am in agreement with Tom Ray to the extent that Classical Mechanics CAN evolve to Quantum Mechanics, but I don't go so far as to say it always does so. It seems to me that there is in reality, something by itself that gives rise to probabilities in any assemblage of great numbers of discrete events, and in that the Wave Function is not what we would commonly call a physically real 'thing'. Rather something that CAN become a real physical event. If that is ever found, then quantum computing would become feasible where now it is really only mathelogical data compactification which is what the NASDAQ will bank on after Moore's Law peters out (soon).

      You condense quite a lot in the brief paragraph content on auditory interpretation, that has piqued my interest. The arbitrary 'time window' is a bit similar to current thinking about Deja Vu where our perception of passage of time is not chronological in the strict sense, and here I think Peter's DFM theory which employs cosine transform is in some way illustrative. While he argues that the helical model can produce results equivalent to QM correlations, I do not see where there is a mechanical apparatus which differentiates where one wave event stops and another wavelength begins, which is not an arbitrary assignment of observer position. (Here we go!)

      Minkowski, blocktime, light-cones and stepping stones all have a place not a privileged position, I agree. r^2 resolves to a two dimensional surface of time dependent correlations, whether quantum or classical. Useful for some purposes but not something that evokes in my mind any full conception of reality.

      I've now waded in a deep as I dare and still draw air, so let me go back to my beach towel and watch and learn. It's a pleasure. jrc

      I'm going to assume that wave-functions are real things. It is a much more defensible position, more so than MWI. It's better than "I have no idea." As for epiphenomena having illusions creating consciousness, it all sounds pretty vague. It is more likely that ghosts and spirits do exist, but that the evidence is getting mixed in with other stuff.

      jcr,

      In order to avoid that our discussion peters out, I just clarify that Peter J. didn't at all deal with cosine transformation. Did Robert McEachern already utter himself to the question CT vs. FT?

      You are right, my suspicion that, in contrast to Pauli's opinion, the complex representations are redundant not just in classical physics but also in quantum physics does not yet answer the question why quantum but possibly the question why Schroedinger introduced a complex wave function. He revealed his thoughts in his fourth communication in 1924. I see Heisenberg's equivalent musing based on the same fallacy.

      Hegel denied the existence of atoms. Mach and Ostwald considered atoms for quite a while as mere imaginations without reality. I would like to cautiously answer the question why quantum by pointing to those few experimental results that don't rely on possibly questionable methods like careless application of Fourier transformation.

      Eckard

      If the wavefunction is ontological, which wavefunction is the real thing? The complex number wavefunction, or the quaternionic wavefunction? Both complex quantum mechanics and quanternionic quantum mechanics give the same predictions for the hydrogen atom. A pure state in complex quantum mechanics is defined up to a phase (a unit complex number) and a pure state in quaternionic quantum mechanics is defined up to a unit quaternion and so the two wavefunctions assign different values at the same space-time point. How can the wavefunction be ontological under this circumstance?

      That is a very smart question, and the answer is: I don't know. I am a spiritualist, and so I am more comfortable with the existence of an aether if I can throw out the Michelson-Morley experiment, and replace it with some kind of wave-function aether filled with the Higgs field, virtual photon E&M field, etc. I think this interpretation of quantum mechanics makes more sense that the MWI interpretation, or just saying, "I don't know". If the aether is made out of ontological wave-functions, then how is that so different from quantum mechanics, quantum field theory and the Higgs field?

      Eckard,

      I'll not speak for Pete, but in earlier discussions Robert made the point that Fourier Transforms as commonly applied cannot extend naturally from the Bohr model Quantum Leap. I would encourage him to reiterate here from his own expertise in FT. To sum-up, his argument is that they are applied from an arbitrary start condition and only condense the observed variation of phase into a modulated waveform that doesn't extend as a continuous transformation from conditions inherent to the emission source, nor give any information as to what those conditions might be. I very much agree.

      In case I'm anonymous (anon) some mass merchandiser bot tracking my usage (to better serve me) logs me out before I can submit a post. I have to log in to my IP and to FQXi ... and do it all over again. My guess is my purchase of a cheap Lenovo is tracked by Best Buy, NSA, and the Chinese People's Army. Hi Spooks! jrc

      18% of Americans have seen ghosts.

      http://www.pewresearch.org/fact-tank/2013/10/30/18-of-americans-say-theyve-seen-a-ghost/

      If 18% of Americans are delusional, then why is our country so productive? So wealthy? So well off? Can someone explain that?

      Florin,

      It is nice to hear from you. It has unfortunately been a while since I went to your website. I had to reinstall browser and lost the bookmark.

      The example with quaternionic QM is interesting. This is the quaternion Dirac equation and the model of the H-atom is a Euclidean form of gravitation. The complex wave function for a system is equivalent up to a phase, and for quaternions they are equivalent up to multiplication by any quaternion, not just the unit quaternion --- at least as I recall. We could write the quaternion wave function as

      Ψ = c_1i + c_2j + c_3k + c_41

      Expanded in the quaternion basis i, j, k, 1. This is equivalent under multiplication by a quaternion, just as the wave function gives equivalent physics when multiplied by a c-number or phase. So for simplicity multiply this by the quaternion i to get

      iΨ = c_1i*i + c_2i*j + c_3i*k + c_4i

      = -c_11 + c_2k - c_3j + c_4i

      which is just an SO(4) rotation in the basis of elements. Of course QM and physics is invariant under changes of coordinates.

      In point of fact the Dirac operator and the quaternion function are both the same thing --- quaternions. The action of the Dirac operator on the quantum field quaternion is equivalent to the cohomology condition ψψ = 0. This is known as the Pauli exclusion principle.

      The statement that the wave function is real does have this odd implication that all complex numbers are equal to a quaternion. Mathematically this is strange, and even without quaternions the wave function being real means complex numbers are all real. Physically the nonlocal properties of QM simply can't be reduced to a classical realization. We might even go so far as to say that classical physics is an illusion. We know it is an illusion because it is falsified outside of certain domains of applicability, such as atomic physics.

      Cheers LC

        Jason,

        The Higgs field is a quantum field, and it fits very well within the quantum paradigm of physics. The Higgs field though has a quartic potential which makes it different from a scalar field with just quadratic potential. For the quadratic potential the potential function has a single minimum point, which means that to get a particle orbiting around it requires the input of energy. The quantization of the field means these orbits come in discrete steps. For the quartic function there is a circle as the minimum of the potential, what might be thought of as the trough of the Mexican hat. This means under tiny amounts of energy you can set up an orbit. There is then a vast degeneracy of quantum states here that fill up a condensate. This condensate can couple in with certain particles, such as the W and Z particles of the weak interactions. This coupling might be thought of as the Whiggs and the Zhiggs (sounds like the British party of old and the Zh has a Russian sound). This gives the Z and W its mass.

        Something happens when this happens. Gauge fields with a massless gauge boson have transverse degrees of freedom, two degrees per particle. A massive particle has a longitudinal degree of freedom. The coupling with the Higgs field gives the W and Z particles this extra degree of freedom.

        This was proposed because a quantum field with mass has this longitudinal degree of freeom, and at very high energy this field effect has anomalous propagations --- it propagates faster than light. So Higgs, Englert, Kibble and others proposed this mechanism so that massive bosons of the weak interaction could be massless at high energy. This prevents the quantum field theory from becoming sick.

        Cheers LC

          Jason,

          I think to be honest the United State of America would not have become the dominant world power without World War II. I honestly think this country would have become a somewhat better off English speaking form of a nation similar to those seen in Latin America in the 20th century. WWII caused many scientists to leave Germany and Europe to the United States of America, and remember Enrico Fermi got the first sustained chain reaction. Also the war demolished the economies of every developed nation except the United States. Highly advanced nations, in particular Germany, but also France, Italy and others were economically ruined with the war. Even Britain remained on war rations for almost 10 years after the war. The Soviet Union was brutally ruined, and barely made it through the midpoint of the war. The US economy surged forwards with no competition.

          Since the reconstruction of Europe and East Asia, ending around 1970 or so, the US has been declining consistently, and with virtually all metrics from educational levels, to productivity per capita to internet connectivity relative to the rest of the world. The following little clip from the program "The Newsroom" sort of captures the nature of the problem

          https://www.youtube.com/watch?v=1zqOYBabXmA

          Americans are behind on metrics such as education and we are a people that have traditionally been low on the educational and intellectual scale. There is a long tradition of know-nothingness in this nation, and this has been hobbling the country. Of late this stuff has been politically popular. We also have trends of xenophobia, and now the right winged panic-mongerers are screaming about a wave of immigrants --- who happen to be children. They are kids for ^&%*#$@ sake, not terrorists! There are these sick trends in this country, they have been with us for quite a while and are now very rampant, similar to the early 1950s with greater durability.

          Are we really that great?

          LC

            jrc,

            Robert is right: Application of FT requires an arbitrarily chosen "starting" point t=0 of reference to which phase refers too. This is the primary deviation from reality. While time spans between two points, between an event-related starting point (1), and an observer-related current endpoint (2), the direction of view for FT is opposite to that for an observer. FT refers to (1) and looks from there ahead toward (2). The ear is the observer and obeys causality. Therefore it refers to point (2) of observation and looks from this current moment, the now, backward to what already happened, i.e. to point (1).

            This logically compelling in common sense physiology is not agreeable with the idea that all time, i.e. the entity of all events, a priori exists and extends bilaterally between infinitely far past and infinitely far future.

            In order to restrict the analysis to already existing data, avoid the necessity to arbitrarily choose a reference point, and therewith create unnecessary redundancy, FT can equivalently be replaced by the CT, which unilaterally extends to the endpoint (2), the now. Robert might not yet trust in this implication because it is not yet generally accepted, not even among the experts of signal processing. Of course, CT does not allow phase shift, and it fails in the unrealistic case of a sin function.

            Eckard

            Eckard

            Yes, the start-point vs end-point measurement is what makes the seemingly paradoxical nature of SR so frustrating. My answer has been to postulate that energy density varies in direct proportion to true velocity across the wave length as an acceleration/deceleration event. I don't want to abuse the forum in self-promotion, but would argue that the constancy of light velocity is properly measured relative to the waveform itself rather that in relation only from the start or end point of observation. Then SR is both demystified and generally co-variant in terms of energy density. jrc