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Rob, LC,

I guess Eddington was correct when stating: "experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation."

Maybe, the recently claimed at Havard evidence for the BB was premature? Maybe, at least a few of the unwelcome argument I uttered aren't unfounded? My primary concern is to possibly reveal very basic mistakes affecting the relationship between mathematics and physics.

Yes Rob, application of Fourier transformation is to blame.

"How can one integrate over all of time, if one does not know the future?" Heaviside's analytical continuation cheats us: The mirrored past is similar to but essentially different from the open future. I beg for getting aware of what we are doing.

Yes LC, "That quantum mechanics is unitary is equivalent to saying it is deterministic". I see the property to be unitary closely related to the likewise unphysical ideal property to be infinite. While a point, a line, the number pi, etc. are strictly speaking just ideals they are nonetheless common prectice as to describe physical systems. Scruples a la Hjelmslev are unfounded. Moreover, history shows that even slightly dirty mathematics adopted from Leibniz, Cauchy, Dedekind, and Heaviside proved utterly useful. Quantum theories obviously led to valuable applications in contrast to SR which merely created paradoxes. Maybe, some oddities that occur with quantum theories will vanish when we accept that the real-valued cosine transformation may in principle fit better than the complex Fourier transformation.

Eckard Blumschein

Isn't it much simpler just to say that wave-functions are real things, and that they have energy states and momentum states? That way you don't have to split the universe into an infinite number of branches to represent the eigenstates. Isn't it easier just to say that wave-functions exist?

As fun as a many world interpretation might be to some people, it would flagrantly violate conservation of energy if every universe in the branch is real and solid. For that reason, the MWI might be literally impossible.

In contrast, if wave-functions are assumed to be real things, then there could be this nebulous aether of wave-functions that is completely undetectable, unpredictable and mysterious. Physicists will hate it. But it being very subtle, it also want cause any big problems for physicists to have to explain.

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The second Law of Thermodynamics holds in a CLOSED system, which does not necessitate that universally spacetime is itself closed. Given the irrationality of pi, if we accept our mathematics to be true enough to reality, it is quite acceptable to conjecture that the only differernce between time and space to be that deficit of radial length resulting from the circumference of a sphere never quite being exactly proportional to any radii constructed to ascertain that a change in volume is physically uniform. If the elusive 'Quantum' realistically exists, it might be found in that relative difference. Energy could then be the creative result of such a physically coherent, yet distinct stress of spatial difference and the relative covariance would be the source of a continuous sustaining creation of energy. This is simply a matter of treating Energy rather than Time as emergent. It is a long way from the laboratory of Lavoisier in yesteryear, to the frontier of inflationary cosmology tomorrow. Bye, now. jrc

Please forgive me for saying the obvious, but some of these explanations of reality sound like a mathematical snowstorm that doesn't actually mean anything. The best explanation for everything that we observe, the quantum fields, the Higgs fields, the encounters with ghosts, is that the quantum vacuum is made of wave-functions that really do exist in some ethereal way, and that the ghosts that people witness are probably real things.

Wave functions are real things!!! That is the simplest and best explanation for quantum mechanics.

    I'm not the only one who thinks that wave functions are real things.

    http://arstechnica.com/science/2011/11/the-insanely-weird-quantum-wave-function-might-be-real-after-all/

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    Jason,

    "Wave functions are real things"

    I tend to agree, energetically of course. jrc

      Ray,

      How can wave functions be real, when they are represented as complex valued functions. They are not even mathematically real.

      The eigenvalues of QM are determined by Hermitean matrices or operators. These eigenvalues are then by definition real c-numbers that correspond to things measured.

      In MWI the amount of mass-energy is constant. Each eigen-branched world is weighted by a probability and the Born rule permits a conservation of mass-energy. This is the case even though there is the appearance of being along only one world and not many.

      LC

      Lawrence,

      Re "The two slit experiment" (Jun. 21, 2014 @ 21:52 GMT): As you say, "when one makes a measurement...the modulus square of those amplitudes give the PROBABILITY of a certain outcome". Quantum mechanics gives very definite PROBABILITIES for INDIVIDUAL outcomes for these particles. So what is definite about reality is its possibility/probability: possibility from the point of view of the particle/subject, probability from the point of view of the observer. So claiming that the situation is "completely deterministic" is to misrepresent things.

      You actually admit to the possibilities inherent in reality when you resort to the "Everett Many Worlds Interpretation", completely ignoring the Ockham's Razor principle. So naturally, you conclude by taking a mysterian position on the nature of reality.

      You are wrong about consciousness being an "epiphenomenon that generates this illusion". Subjective experience/consciousness is not separate from information about reality: I contend that at the level of a particle, this basic-level information is of mass, charge and law-of-nature relationship. This information is essential to the functioning of reality: consciousness is essential to the functioning of reality.

      Rather than giving up and taking a mysterian position, surely, the solution is to free up a little: maybe nature is not quite the tame mechanism that you envisage.

      Lorraine

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      I still find the MWI interpretation of quantum mechanics to be impossible. You are asking me to believe that every time a new eigenstate appears, a new universe (which has an energy content of hundreds of billions of galaxies) just pops into existence. It does so without us even noticing it. It violates conservation of energy flagrantly. Not to mention that the information content of an entire universe has to be duplicated and moved away faster than light so that nobody notices. Physicists believe that, but are shocked and horrified at the idea that the wave-function is a real thing that is perhaps impossible to detect and is very mysterious. Why wouldn't that be the preferred interpretation?

      John, you're a radical! lol Watch out! The idea that wave-functions are real things is heresy as far as the physics community is concerned.

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      LC,

      I would like to learn rather than claiming to be correct. While I understand that and why Hermitian matrices are real-valued, and I very much appreciate your view, I am not sure what you meant with real c-numbers. Did you mean the real parts of complex numbers?

      Incidentally, iIrc, Gauss wrote that he regrets that imaginary numbers are called imaginary. He meant that they are quite normal numbers, and his attitude did perhaps influence the further development of mathematics as well as of physics. Gauss correctly argued that negative numbers are justified if there exists something exactly opposite that compensates a positive measure. Dedekind and Riemann were pupils of Gauss. Georg Cantor added naivety ans charisma to their detour from Euclid's and Galileo's rationality.

      As a teacher of EE, I operated for more than four decades with imaginary items. However, I was always aware that they are just mathematical tools as to describe something real.

      Already Leibniz called the infinites and the infinitesimals well-founded fictions with a fundamentum in re as also is i. I conclude: he did not yet understand that every number is something ideal.

      Eckard

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      Eckard,

      "I question Minkowski's spacetime and the necessity to integrate over future time too when analyzing past data."

      Yes, I think I follow that argument. Really it goes back to the ambiguity of what r^2 is supposed to represent, and in reality at best only trigometrically. I have always found it as contrary to comprehension as the 'rubber sheet' illustration of GR, to look at an illustration of the universe 'timeline' that has the shape of a tall plastic cup that has been picked up from sitting on a hotplate.

      Also, I seldom comment due to my lamentable lack of advanced math, but do often find help in understanding from many of your learned contributions. I do wish you and Tom could find common ground, though he is theoretical and engineers are more practical. My best wishes to all. jrc

        I can't help but think that if a ghost is going to produce some phenomena, it has to create an equivalent wave-function/quantum field. To do so, it has to generate the appropriate V(x,y,z,t) in order to get a psi-wave-function that can emit red photons from the eyes (for the glowing red eyes appearance), or appropriate momentum states so that the ghost can properly shove somebody. I'm just using an educated guess, but a spirit is something feels and experiences. To that end, maybe the ghost/spirit has to feel or experience the V(x,y,z,t) that it generates; maybe it feels it as pain or discomfort. But when it doe gnereate a wave-function with energy and momentum states, then it has to obtain energy from somewhere.

        I am not going to engage in too much discussion on "reality" from a metaphysical perspective, where terms like reify and ontology and the like come into play. Wave functions though are not real in a strict sense of having real valued measurable properties. If one wants to engage in metaphysical conjectures about reality other than this rather operational one, then fine. I just tend not to take these that seriously.

        LC

        I think that attitude is blocking the physics community from exploring a whole area of theoretical physics that could describe parts of reality that you are all uncomfortable with. For instance, I can explain the physics of a ghost. Let me show you. Virtual photons make electric and magnetic fields work. If a ghost can get access to the virtual photons, if it has great skill it can create a potential energy V(r,t) without using charged particles. If, as I have stated, wave-functions are real things even if they're not measurable directly, then a wave-function will come into existence by virtue of the time dependent Schrodinger equation. This wave-function will have energy states and momentum states that the ghost has to fill with energy (by creating cold spots, siphoning from batteries or from people). Then it can use that energy to move objects, radiate photons that look like scary red eyes, shove people down stairs and do all the spooky poltergeist phenomena.

        Can anyone tell me the specific reason for why this kind of a ghost would contradict known physics?

        By the way, I'm not too interested in philosophy either. I want to understand how observables relate to physics. If someone is claiming to see something that violates physics, I want to know "how" it violates known physics. Physicist "scoffing" at paranormal phenomena is shackling humanity to the dark ages.

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        If there is a choice, then causation is fundamental to the construction of physics. If the foundation of physics is causal, then entropy is an indication of moving from one causal system to another, not characterized completely by energy. Entropy is an indication of the dis-coordinate relationship between time and space.

        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.