In an old paper at IJTP, Wim B. Drees argues against Hawking-Hartle's interpretation that wavefunction of the universe implies the probability for the universe to appear from nothing. What do you think?
http://www.drees.nl/publications%20eng/Interpretation%20of%20the%20wavefunction.pdf
The Universe can't appear from nothing since it would break the conservation of energy. It is possible only during a short time because of the uncertainty relation of Heisenberg, but a very short time indeed.
A little off your exact question but an interesting point is that using the "wavefunction of the observable universe" one could loosely say that you can "derive the Hubble constant". More accurately what I mean by this is have by treating the entire observable universe as a quantum wavefunction one gets an expansion rate at the present epoch which is of the same order as the Hubble constant. Superimposing the wavefunction expansion on space-time GR expansion in an Einstein-de Sitter scenario also predicts dark energy, aka cosmic acceleration, with a correct switch over time for deceleration to acceleration. When I discovered this I nearly fell off my seat! Of course the match may just be a coincidence, but it is a rather neat way to explain cosmic acceleration. If you are interested you can read the theory at http://www.aip.org.au/info/sites/default/files/Congress2012/01._ERNEST_AIP2012.pdf. If this turns out to be the cause of dark energy then it would certainly add weight to the voracity of the Hawking-Hartle approach.
It does not mean to appear from nothing with the absolute meaning of "nothing", i.e. something to which we can adscribe no properties. In fact, the universe would appear (in that paper and in many others) from the Euclidean region of the superspace (the configuration space of all possible geometries and matter fields), but from a physical point of view the Euclidean region, with an imaginary time variable, is not physical in the sense that no matter or energy field could be measured or exist. In that sense, it can be understood as nothing (physical), but the mathematical framework may cover more than what is called "physical reality". It is not much different to what happend in general in quantum physics. The fact of whether the wave function of a particle( or a field or whatever) is something "real" or just a mathematical construct from which we can obtain physical (i.e. measurable) properties is a matter of heated discussions in phiosophy of physics. My view is that it is not of much importance if we actually know what we are exactly meaning by the words we use and the properties we can eventually meassure. In any case, the H-H proposal entails a possible (and mathematically more or less tractable) explanation for the origin of the universe, according to the currently known laws of physics, and in some sense, it opened the door to a new whole branch of cosmology and physics allowing to make further developments on the subject (which is one of the best things that a physical proposal can do).
Of course, the question is far from being totally settled. Let me point out that the multiverse (the set of all possible universes, which need not to be located in any space-time structure), for instance, would change many of the preconceptions usually made regarding the birth of the universe. For instance, Gott and Li (see the link) propose that the universe may even be its own mother, and many other proposals can be envisaged within such a novel paradigm. Broadly speaking, we could pose two options: either the universe is created from some space-time structure, which just put the question further to the origin of that space-time structure, or the universe is created from another (non spatial and temporal) structure, where it does not make sense to ask for the origin of the universe, in the temporal sense, because time would be created with the universe itself.
http://arxiv.org/abs/astro-ph/9712344
One should define what Universe or quantum state of Universe means first. Theoreticians tend to have different views about this!
In QFT approach one thinks space-time as a fixed arena of physics and empty Minkowski space would be counterpart for "physical nothing". Already Wheeler proposed a more general framework leading to the notion of wave function of the Universe.
In my own TGD framework relies zero energy ontology replacing ordinary positive energy ontology. Quantum states have vanishing total conserved quantum numbers and decompose to pairs of positive and negative energy parts. Any zero energy state is in principle creatable from vacuum in quantum jump replacing Universe with a new one. Replacement is possible, not creation from nothingness.
Zero energy states form a scale hierarchy assignable to causal diamonds (CDs) whose M^4 projection is intersection of future and past directed light-cones (Penrose diagram). Space-time surface in given scale connects 3-surfaces at oppoite light-like boundaries of CDs, which define "sub-Universes", kind of spotlights of consciousness.
Quantum superpositions of space-time surfaces satisfying classical field equations inside CDs define zero energy states. The 3D quantum states at opposite boundaries of CD possess opposite conserved quantum numbers. Any state of this kind can be created from vacuum without breaking conservation laws. In positive energy ontology creation would do this. In QFT picture zero energy state translates to quantum fluctuation and could be also interpreted as analog of physical event: initial/final state-positive/negative energy part of state. ZEO is consistent with crossing symmetry.
Appearance of universe from nothing is possible only in this sense. After and before every quantum jump there is zero energy state. Sub-CDs can pop up from nothing and disappear just like mental images appear and disappear. Entire Universe corresponds to the union of all CDs of various length scales.
Dear Victor,
There is not the wave function of the universe, there is the wave function of the gravitational field. In this case, the gravitational fields are limited in space and can change sign. For the solar system they are described by one value of G, for galaxies – the another value G, for metagalaxy - third. Some of these issues are discussed in the article "Femtotechnologies. Step I Atom Hydrogen" http://vixra.org/abs/1306.0014
If such an animal like the wave function of the universe makes sense, then this has to be part of an interpretation which differs from the minimal one, where the wave function is a state created by a certain preparation procedure - a measurement which has given some result, measured by some device outside.
There are such interpretations, in particular de Broglie-Bohm. Here, the wave function of the universe is usually interpreted as some really existing field. But this is not obligatory. My own proposal is described in http://arxiv.org/abs/1103.3506 where it is only something which describes information available about the state of the universe (a Bayesian interpretation).
There is also many worlds, which has a wave function of the universe, but the netiquette forbids me to say what I think about many worlds.
"Probability of the universe to appear from nothing" is IMHO simply nonsense - without reading the paper where this is claimed.
good question, how do we even know that the universe has a wavefunction?
It is simply an extrapolation of quantum theory. To extrapolate existing theories to the extremal points is, in itself, good scientific practice - taken to the extreme, it becomes easier to identify the weak points.
Agree. To me wave function of Universe or its proper variant is ok. However, generalising straightforwardly the non-relativistic Hamiltonian formalism to general relativity procedure as is done in first attempts to quantise GRT looks to me highly non-realistic. One well-known implication is loss of time.
There is not such a thing like 'wavefunction of universe', We have over-estimate linear algebraic tools like quantizing practise.
I think the mathematical accuracy of a physical model is inversely proportional to the number of bodies contained in the model. This is the reason why hydrogen atom model with two bodies and Newtonian gravity model with two body has maximum accuracy. Models of heavier atoms and multibody gravitational systems are less accurate. This is also one of the principle reason for failure of general relativity at Planck energy. From this point of view the wave function of the universe cannot provide a very reliable mathematical model.
@Demetris, Vikram and Prof. Matti Pitkanen: thanks for your answers, and i agree with you that the wavefunction of the Universe is problematic, not only because it extends the probabilistic intepretation of QM which is also debatable since the time of Schrodinger and Einstein, but also because it does not explain anything. This is similar to the so called Wheeler DeWitt equation which does not explain anything. What do you think? Best wishes
Wheeler de Witt equation is derived using the highly non-realistic assumption that non-relativistic quantisation rules apply when the number of degrees of freedom is infinite so that I cannot take it seriously. One must remember that at that time not much was known about quantisation of infinite-D systems.
Wave function is claimed to completely describe the reality. The wave function is not given. One can not write \Psi without any particular form and talk about the complete description of all there is. Is the Grand Truth the Psi? The latter is nothing, because is not presented as function, it is only a symbol. I well might write "Gamma" and say, that it is wave-function of Love.
Not sure what you are writing Dmitri, perhaps it's because of the odd way you put English together - in any event, it is well known that we cannot write out the wave function of any but the simplest physical systems (such as a hydrogen atom.)
This limitation has nothing to do with the fact that all systems have a wave function, and that there is a hierarchy of wave functions in nature - it has to do with our inability to deal with the complexity of the math.
It is easy to demonstrate that a physical system has an associated wave function; by the same token, explicitly writing out this wave function is most often fiendishly difficult. Perhaps if we had 20-gallon brains and many trillions of neurons it would be easier.
@ Victor, I'm not sure that the wave function 'explains anything', as you put it: it just is. A wave function is nothing but the mathematical signature of something that is. The probabilistic interpretation - or rather, use - of a wave function only occurs when its integration boundaries are set within a subset of the available space where that something is; when the integration boundaries are set to the full extent of the available space (typically -∞ to +∞ ) , then the resulting value is 1 - simply meaning that the something in question exists.
Dear H Chris Ransford, thank You. 1) The people are different: I simply got an unique style and original connection map between the brain cells. 2) The wave function of Universe is hardly possible even in principle, because the scalar particles in Universe assume to have scalar wave function, the vector particles (photons, electrons) have vector wave function, the bosons have Bose-Einstein statistics, but fermions have Fermi-Dirac statistics. 3) But let's put it all aside, how looks the wave function of the Friedman Flat Universe, if it would be filled with dust-like medium. I speak about large scale, not about the grains of dust. Can there be two levels of the wave function, I mean, what on the macro-scale the wave function asymptotically assumes much more simple form? If Yes, I am sure the Hawking can present it, if the Bohr's vision of Quantum Mechanics is correct.
Suppose we have wave function of an electron E^i and function of neutrino N^k, the system function can not be the tensor S^{ik}=E^i N^k (because it is never heard), thus, shall be the sum S^{i}=E^i + N^i. Then suppose you have scalar particle too, logically you must add its wave function f: E^i + N^i + f. But latter is impossible: it violates the vector algebra. Thus, there is no wave function of Universe or some other system.
Consider an observer watching a man approaching a cross road running east to west. For the observer the probability of the man going east or west is 50-50. But the man has made up his mind to go west. So the moment the man turns west the wave function of the observer's theory collapses. Here we can see that the probabilistic interpretation of the phenomenon by the observer arise due to his lack of knowledge of the working of the mind and consciousness of the man under observation. Same is the case with the particle motion in quantum mechanics. Someone may ask whether particles have anything to do with consciousness? A unique aspect of consciousness is that one can be sure about one's own consciousness but about others he/she can only make a guess. Because I have a consciousness therefore other people behaving like me must also have consciousness. Similarly we can make a general guess that particles of physics do not have consciousness but we can never be 100% sure about our guess.
Suppose the entire universe at the beginning is a motionless consciousness without any boundary. It will appear to physicist as nothingness. Wheeler de Witt equation is H\psi=0 which also imply no motion and zero energy. So nothingness is of the energy not the consciousness. When consciousnes begins to move it becomes quanta of energy and you immediately notice both the motion and the energy.
"Wheeler de Witt equation is H\psi=0 which also imply no motion and zero energy."
Objection from Wikipedia: "the Hamiltonian no longer determines evolution of the system, so the Schrödinger equation \hat{H} |\psi\rangle = i \hbar \partial / \partial t |\psi\rangle no longer applies."
Dmitri, generally speaking I'd be rather leery of quoting Wikipedia ... Quoting some recognized, peer-reviewed textbook or other, is usually the ticket here.
Just read your above answer - I'm a native speaker of English, perhaps it has more to do with fluency with the language rather than brain cells? For instance, the proper English is not 'the people are different', but 'people are different', although it's clear what you are trying to say in this instance. I would certainly not venture to try Estonian ....
I am sorry I do not follow at all your line of argument . Wave functions are embedded within a Schrödinger equation applying to particles, either individually or as constituents of a system. As long as decoherence has not set in, an established Schrödinger continues to be valid (as is experimentally confirmed by Alain Aspect's and Nicolas Gisin's experiments)
Dear H Chris Ransford, thank You.
1) nevertheless the expression "THE people are different" is correct within my worldview. I believe, many people are essentially of the same stuff. Thus, with "the" I refer to DIFFERENT ones.
2) Yes, You have missed my point. Suppose you have two particles: an electron (E^i) and theoretical sterile neutrino (N^k) with non-zero mass. Particles are confined to some area. There is no interaction at all, however the two wave functions (E^i, N^k) do cover each other. How is expressed the wave function (S^i = f(E^i, N^k)) of the system?
Dear Victor, the term 'wavefunction of the universe' could mean next things:
Do you honestly believe that the 2. interpretation above has a meaning? If not, then your question has been answered...
It is possible to treat the universe as an acceleratedly expanding self-gravitating systems consisting of ordinary matter(4%), dark matter (26%), and dark energy(70%). This self-gravitating system is an outcome of an effective theory of quantum gravity. In this Quantum Gravity Theory one starts with GTR and ends up with the Hamiltonian of a self-gravitating system.The wavefunction of the universe is constructed through the single particle wavefunctions of its constituent particles. This formalism considers the universe as any other system in quantum mechanics and it reproduces many results including a relation connecting time, temperature and the cosmological constant of the universe. The value of the cosmological constant is in agreement with the value determined otherwise. No need of considering the Wheeler de Witt equation H\psi=0.
@Dmitri Martila.
In Wheeler DeWitt equation time does not play any role. The equation can be derived using gravitational action around 3-metric boundary on which matter field already exists. The wavefunction \psi contains all information about the geometry and matter content of the universe. Reemergence of time requires the tools of decoherence and clock operators, Hamiltonian also needs to be augmented by momentum constraints. This theory splits up space and time and does not explain how the matter field came into existence to begin with. If the wave function \psi is non zero than Hamiltonian has to be zero. Which means no motion. But if some matter field already existed than energy can never be zero. When energy is replaced by the quantum operator, the time has to come into picture. So there is a contradiction. This is the problem of time in Wheeler DeWitt equation.
In "Perodic quantum gravity and Cosmology" time and Hubble parameter are associated with energy as oscillations or frequency. In the beginning no matter field exists. The only thing that exists is Consciousness (Spirit) which is motionless, which means no oscillations and no time which means no energy because energy is always associated with motion.
@Manuel Morales.
In Western philosophies Universe emerges from insentient matter and much later in the evolution, consciousness pops out as an effect. In Eastern philosophies however, Universe arises from Consciousness (Spirit), degenrates into matter and then evolves and returns back to the Consciousness (Spirit). The Consciousness Himself/Herself/Itself is the Great Cause of the universe which is also the fundamental substance of the universe and is not caused by anything else. This has existed through eternity and will exist through eternity to come. Following link gives more details.
Article Unified field of consciousness
@Vikram Zaveri
It is good, that we are not atheists. These deluded people are very intrusive. It is just the beginning: "Rhymes that keep their secrets. Will unfold behind the clouds. And there upon the rainbow. Is the answer to a never ending story" (film "Never Ending Story").
This single hypothetical function describes the space of states of the Uni, niether less nor greater. The probabilities are in our interpretation, it's secondary quest.
@Vikram, Manuel, Demetris, H. Chris Ranford, Arno, Dmitry, Subodha, Dmitri and others: thank you for all your answers.
@Demetris: in my humble opinion, Hartle-Hawking's wave model of the Universe seems interesting, but i do not accept their probabilistic interpretation. I do not claim that i have the same thoughts with Einstein, but i cannot resist to say that God seems to not play dice. Thanks
Lee Smolin in “Elegance and Enigma: The Quantum Interviews”: "[...] To put it differently, the only interpretations of quantum mechanics that make sense to me are those that treat quantum mechanics as a theory of the information that observers in one subsystem of the universe can have about another subsystem. This makes it seem likely that quantum mechanics is an approximation of another theory, which might apply to the whole universe and not just to subsystems of it. [...]"
Any axiomatic theory is incomplete. The Aristotle model has provided, long ago, a good prediction, but not so far, as wanted. No fate, apart the Laplace demon, whom also should be modified in detail.
There's an interesting discussion of this theme, by David Z Albert and Steven French in the book 'The Wave Function', edited by Alyssa Ney & David Albert - much too long to summarize here, but I can only recommend the book for an interesting discussion
@Dmitry and Dr. H. Chris Ransford: thank you for your answer. best wishes
Wave function is a statistical function, that can not be derived from a single event.
That can be true if it can be shown that the total energy of the Universe is zero. The conservation of energy also holds in quantum mechanics.
A virtual particle pair can arise from nothing, but not a real one. However, for the virtual pair to have some observable effet, there must be something to break the symmetry, otherwise all the virtual pair creations cancel together and the probability is zero.
That's an instance where science is made a religion, but with easy falsifiable wrong reasoning.
Actually, the objection of Drees is not on the physical ground. Hawking purports that their model makes a creator completely unnecessary. But if the Universe arose by a quantum transition from a particular state (which is only described by very different laws from our ordinary reality, but is not "nothing" in any way,) this state must be "finely tuned" and can't be anything.
The Hawking-Hartle model doesn't escape the infinite causal chain conundrum. That is the eternal quest of a primary cause, that is called "God" by some metaphysicists (especially Leibniz.) The merit of the model is only to show that there is not necessarily an origin for the time, although there is one for the Universe, but the old dream that science will obliterate religion still have to wait, probably an infinite time.
Here is a working link to Drees' paper:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.521.1820&rep=rep1&type=pdf
In order to share a new point of view let me notice that the so-called wave function of the universe, i.e. the wave function of the spacetime and the matter fields all together, can also be seen as a field that “propagates” in the superspace of geometries and matter field configurations, being the Wheeler-DeWitt equation the corresponding wave equation. Within this framework (the so-called third quantization formalism) creation and annihilation operators of spacetimes and matter field configurations can be defined (at least in superspaces with some degree of symmetry) and they describe the creation and the annihilation of universes in a parallel way as they describe the creation and the annihilation of particles in a quantum field theory. From that point of view, the interpretation of the wave function of the spacetime and matter fields (i.e. the wave function of the universe) would parallel the interpretation of any other field in a quantum field theory.
Thanks Salvador, much appreciated. There is an issue though with the WFOTU which I'm trying to address in a book I'm currently writing (which will be my third and final book on the theme of the nature of (ultimate) reality.
The issue is that when you carry out the ʃΨΨ*dσ operation on the wave function Ψ you normally end up with a probability of presence - but the probability of presence makes sense only if there is something else - in other words ʃΨΨ*dσ makes sense if you keep some last variable external to Ψ, and then when you bring in the last element, therby incorporating the whole universe, then the meaning of ʃΨΨ*dσ breaks down (that's the second instance of mathematics breaking down, after Cantor's antinomy) - although the mathematical operation itself is still legitimate.
To solve this, some say, somewhat glibly, that 'the WF of the universe does not exist', which of course is pat and does not begin to resolve the issue. The second way to deal with it is to posit something outside the known universe (so that the meaning of ʃΨΨ*dσ does not abruptly and inexplicably breaks down when you bring in the last bit of the universe), but then you immediately end up in an infinite regress, and you can only conclude that there is an infinite universe/multiverse out there.
There are ways to solve this, which is what my new book will be all about
Thanks Chris. I think however that there are different issues at hand here.
One is the probability meaning that we want to ascribe to the wave function of the universe. I would say that it entails the probability of existence of the spacetime and the matter fields rather than the probability of presence, because as you say the latter implies the existence of something else, and the universe is usually that “something else”, but of course, this is quite dependent on what we mean by the word “something” (something physical, something mathematical, something metaphysical…).
The normalization problems of the wave function imply that we can only consider the relative probabilities for the creation of different configurations of the spacetime and the matter fields. However, in my view, it is not of much importance the particular value of these probabilities as far as they are different from zero because we could well be a very strange phenomena of nature violating no physical law at all, so the important thing, from the point of view of the existence of the universe, is that those probabilities are strictly different from zero. That’s the only thing we need to exist (for a physical explanation of our existence, at least).
A different thing is the question of “where” does the universe come from? If by “where” we mean something physical, i.e. something that can ultimately be measured (or spoken, if one prefers Bell’s nomenclature) in terms of rods and clocks, then, it turns out that it comes from nothing, irrespective of whether this means a point (like in HH paper) or a whole region of the Euclidean regime of the spacetime (which, by the way, is not (physical) spacetime). Of course, this “nothing” does not refer to the absolute meaning of nothing, i.e. something to which ascribe no properties, but just to the classically forbidden region of the spacetime where no physical time exists and, thus, nothing physical exists.
In the context of the third quantization formalism that I mentioned, the multiverse can be seen as the “many-particle” description of the quantum field theory of the wave function that quantum mechanically represents the whole spacetime manifold and the matter fields that propagate therein. It is not exempt from problems but, in that context, it turns out that the ground state of the field is full of virtual pieces of spacetime called universes that pop up from and delve into the quantum foam of the abstract space of spacetime geometries and matter field configurations, the so-called superspace. However, there are no causal relations in the superspace because there is no, in general, a definite time variable, so the universes are not created before or after, or further or closer, because these are terms that only make sense within the context of a single universe (= a piece of spacetime with things in it). A remarkable example of this is the universe proposed by Gott and Li, arXiv:astro-ph/9712344, where the universe is its own mother!)
It is of course, an open and a very complicated question, so at best this would only be one possible but also plausible (physical) explanation. There can be many more acceptable ones, of course. We will be looking forward to your book, sure.
Suppose there is a wave function of the Universe, and we can follow its evolution back in time. That entails two dead ends:
If the Universe is created from this wave function, what created the wave function in the first place?
Quantum mechanics is time reversible, but not in the intuitive way. That is, from the known present measurement outcomes, we can deduce the probabilities of a measurement if it was done at any time in the past, thus including the 'time 0." In other words, there is no well defined initial state.
Because of these inconsistencies, should we say that the Universe has no wave function, or rather that the wave function is a ill-defined concept that is bound to break down in extreme situations? The latter is obviously more plausible, we must be humble and admit that the mystery of the Universe is not yet at our reach.
The wave function of the universe does not depend on time because the time reparametrization invariance of general relativity, nor it is defined in time like the wave function of matter fields propagating in a background spacetime. It does not propagate in a background spacetime and, strictly speaking, it does not evolve in time. In fact, from the point of view of quantum cosmology, time and the quantum mechanics of the matter fields (the Schrödinger equation) are emergent features of the semiclassical regime of the wave function of the universe and not the other way around.
On the other hand, it does not make sense to say that the universe is created from the wave function of the universe in a causal way like “it was first the wave function and then the universe”. It is like one would say that the universe is created by the word “universe” and then ask, what did create the word “universe”? The wave function of the universe describes, in the language of quantum mechanics, the quantum state of the universe.
I totally agree that the universe has a lot of mysteries still to be solved. It is one of the fascinating aspects of it. But let us not create inexistent inconsistencies or artificial debates. Reality has many faces, all of them needed for a complete understanding of it-us, so let us leave the nineteenth century paradigm of “one or another” and, as quantum mechanics may suggest us, consider the “one and the others” paradigm provided that the same question can be posed from many different points of view.
The geometry of space time depends on the distribution of mass, and this distribution evolves in time. When there is a measure and the mass concentrates at one point, that leads to inconsistencies, that's the problem of quantum gravity. The concept of wave function of the Universe is ill-defined because of this very reason, not because the Universe is all that exists.
Claude, not sure I quite understand your answer.
1-The fact remains that the meaning of the operation ʃΨΨ*dσ breaks down entirely the instant you add in the very last element of the universe, although mathematically there is no disruption. How can we interpret the meaning of a mathematical expression abruptly breaking down when the mathematics itself continues to be smooth?
2- Not sure what you mean about 'when there is a measure and the mass concentrates on one point', I take it you mean at the point when the universe is in singularity status (a time when then obviously no measure can be taken, because the singularity would be 'all that exists', and then by definition taking a measure would be impossible because of the very same issue, so we're back to where we were: ill-defined because the singularity (the form of the universe at that point) would be all that exists. You seem to be contradicting yourself?
Besides, Claude, you are missing the point of quantum cosmology because you are thinking on a classical level. The wave function of the universe depends on the geometry and the matter fields, being these two independent variables (the variables of the so-called superspace). They do not depend on each other at the quantum level, as you are assuming. Only when a decoherence process has taken place and the semiclassical regime of the wave function can be considered (i.e. a WKB solution can be considered), is when we can obtain: i) a relation between these variables; ii) a time variable in terms of which the previous relation turns out to the the classical equations (Einstein’s equations), and iii) the Schrödinger equation of the matter fields that propagate in the background spacetime determined by the two former conditions. If you go backward in time, time begin to lose its classical meaning becoming useless in the spacetime foam (see the beautiful paper of Wheeler: “On the nature of quantum geometrodynamics”).
The fact that we don’t have a satisfactory theory of quantum gravity is not an inconsistency of the wave function, I think. Can I ask, why do you want it to be inconsistent?
So there is no satisfactory theory of quantum gravity, therefore all you say is just a speculation. What I say is it is because quantum mechanics, is not a satisfactory theory either, then the wave function is ill-defined. The problem is the same as the measurement problem, when the position of a particle is measured (it mass concentrates at a point, as it were) the geometry of space time must change too, but general relativity is a non linear theory where the superposition principle doesn't apply. In conclusion, there is no language that allows to speak about the wave function of the Universe.
To have some meaning, quantum mechanics requires a classical apparatus outside the quantum system to make a measurement, and without measurement there is no physics since the wave function is "not real." For the wave function of the Universe, there can't be any measurement apparatus, so that even the "probability of the Universe to appear from nothing" is meaningless. But in my opinion that's not a separate problem from the measurement problem.
No, it does not work like that, in my view. The fact that there is no satisfactory theory of quantum gravity, mainly because the solution of the WDW equation is quite complicated in a general case, does not imply that quantum gravity or even less quantum mechanics is inconsistent. It does not imply either that the wave function is ill-defined (I can’t see the logic behind the reasoning). It is like we would conclude that General Relativity is inconsistent because the solutions of Einstein’s equations are really difficult to obtain in a general spacetime with a quite bizarre matter content. It does not make sense at all (at lest to me).
General Relativity is consistent in the sense that it provides us with a consistent explanation in physical terms of phenomena that are not explained by other theories (i.e. Newtonian mechanics). Quantum mechanics is consistent in the sense that it provides us with a consistent explanation for physical phenomena that cannot be explained in a simply way by other theories and, by the way, with an astonishing accurate precision.
The concept of the wave function of the universe comes, as C. Kiefer clearly explains, from the fact that any quantum system is coupled to its environment, which in turn is coupled to another environment and so forth. The extrapolation of this idea leads to the concept of the way function of the universe. In a closed system, the observed, the observer (the measuring apparatus), and the environment are all subsystems of the closed system. Thus, the wave function of the universe must provide a physical description of all these systems once a decoherence process between them has appeared, i.e. in the classical regime. It does not make it to be inconsistent. What is inconsistent, and it is probably here the source of your confusion, is to apply the standard (i.e. xxth century) Copenhagen interpretation of quantum mechanics (which is by itself inconsistent) to a closed system like the universe.
Salvador, I seem you work rather on beliefs. You believe in quantum gravity, in decoherence as a solution of the Copenhagen interpretation, and in the classical limit of quantum mechanics. So be it, but that doesn't make them consistent either. It has been shown that general relativity works, not decoherence (not everyone is convinced) nor quantum gravity. That doesn't make them inconsistent too, agreed. But contrary to what is widely said, the limit of quantum mechanics is not classical mechanics, they are two different theories based on two distinct representations of Poisson algebras; approximations are possible only in some special cases. If the classical limit is needed for quantum gravity to work and for the wave function of the Universe to exist, that may be a fatal difficulty.
I have good reasons to believe that quantum mechanics is not the final answer, even if it is complete in some meaning, that it is not mathematically consistent, and that it is why quantum gravity can't work. In the present state of the art, we can only guess.
Claude, using the formulas of the de Broglie-Bohm approach, the classical limit of quantum theory is not a problem at all. You have a trajectory anyway, the Quantum Potential obviously goes zero for the Planck constant going zero, or the wave function being wide enough, so that the equations become the classical Hamilton-Jacobi equations.