In quantum cosmology, the so-called wave function of the universe is introduced, which is described through the Wheeler-DeWitt equation (Schrödinger equation for the wave function of the universe). This equation does not depend on time, since the total Hamiltonian of the Universe, including the Hamiltonian of the gravitational field, identically vanishes. This means that the universe as a whole does not evolve over time. I searched for an explanation of this paradox in several sources, but did not find an illustrative one. The most obvious was the interpretation that the concept of evolution over time is not applicable to the universe as a whole, since there is no external observer in relation to the universe, and there is no external clock that does not belong to the universe. The wave function contains components that correspond to all possible states of the Universe (all possible geometries, and so on). When we artificially divide the Universe into two parts, one of which is an observer with a clock, and the second is the rest of the Universe, then there is still a connection, correlations between the two parts, because they are parts of one whole. And the states of the apparatus (clock) correlate with different states of the Universe. Thus, a sense of the passage of time and the evolution of the Universe is created. How correctly did I understand this interpretation?
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It’s often said that the problem of time exists because time is treated as absolute in quantum mechanics but not so in General Relativity, see e.g. . However Quantum Field Theory merges QM with Special Relativity, which treats time as relative (time dilation, etc). What actually leads to the problem of time in Quantum Gravity?
105091
Are  and the  really the same thing?  Not too long ago, Susskind and Bousso uploaded the article "" with the thesis that the many-worlds interpretation and the multiverse of eternal inflation are one and the same thing. The parallel worlds of one are exactly the same thing as the parallel worlds of the other.   First, they claim decoherence can't happen over a complete description of the future light-cone of the measurement. Then, they apply that principle to eternal inflation. Without decoherence, superpositions of nucleating bubbles and metastable vacua can't decohere. According to the anthropic principle, most bubbles have no conscious observers, but an exponentially small minority do. Apply black hole complementarity to causal horizons.  Then, somehow, in a way I can't follow, they combine causal diamond worlds into a global multiverse.  Then they claim decoherence is reversible.  My head is spinning. What are your opinions on this paper?
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I've always hit two big stumbling blocks in conceiving of the proof or disproof of  as being even valid idea, let alone an answerable question... I feel I must be misunderstanding some very fundamental things.   Quantum mechanics is deterministic, ignoring the bit where we take our complex number and fudge it into a probability. We use computers to make calculations to provide the predictions of quantum mechanics - how is this not itself a hidden variable theory?   From what I understand the famous Bell theorem and work around it doesn't disprove hidden variable theories, just one specific flavour of them, and even then I am not convinced. I feel like I must be missing something again, because this result seems to me in no way profound... although it certainly fits into the picture of the EPR 'paradox' and is a good demonstration of the validity of QM.  I guess the crux of my problem is that this 'area' really addresses wave function collapse and the problems it causes, but I don't see the need for some collapse mechanism to begin with... again I feel like I am missing something really fundamental.  Apologies if this is a bad question. I have had a look around and there are similar questions, but I don't feel that either of my points are addressed...
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According to special relativity, a photon traveling at the speed of light, does not “experience” time. It is traveling into the future at an infinite rate, right?  That would mean that everything that could ever happen (my death, Trump winning the election, death of sun, end of the universe), has already happened (from the frame of a photon). We're just too "slow" to experience this.  Is this correct? Because that would bring some weird implications about free will, and the very nature of our existence. If everything has already happened, then we're just following a predetermined path.  Edit 1: I'm genuinely fascinated by this topic, however, I am also an idiot with very superficial knowledge, gained mostly from youtube videos and Wikipedia. Bear that in mind :)  Edit 2: The nature of my question seems to leave the realm of physics and cross into a philosophical issue. I was seeking physical explanation, to help answer something of philosophical nature, as both these realms seem to coincide for this particular topic.   Some have pointed out that thinking about the frame of a photon doesn't make sense. Instead, one could assume a spaceship traveling at $0.9999c$.
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Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom. Entanglement with this "apparatus" takes care of the decoherence. It is often said (I can provide references upon request) that the remaining problem is the one of "selection", and this is the point where one invariably invokes something philosophically radical, like many-worlds interpretation.  In the above (pretty standard) context, I am trying to make sense of the following observation. Looking at the measuring system from a statistical mechanics point of view, it seems that triggering a particular macroscopic outcome requires spontaneous symmetry breaking via a (thermodynamically) irreversible transition of the "apparatus" from a metastable to a higher entropy final state. My attitude is that "statistical mechanics point of view" is not far from "decoherent large quantum system".  So, the question is:  Is it fair to say that statistical irreversibility ("the second law") and quantum measurement irreversibility (the "wave-function collapse") are necessarily linked? Can this link be made more concrete (e.g., traced in details in a particular model)? Can you give references to approaches to the measurement problem that explore this connection?
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My confusion about quantum theory is twofold:    I lack an adequate understanding of how the mathematics of quantum theory is supposed to correspond to phenomena in the physical world I still have an incomplete picture in my mind of how cause and effect relationships occur at the quantum level of reality.    This is why phenomena such as "entanglement" make absolutely no sense to me. So, in an attempt to come to some understanding of all of this, I would like to know that if what we conceptualize as a "field" is merely an interaction among particles, and particles themselves are actually fluctuations in "fields", then which comes first, particles or fields?
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It seems to me that there is no such thing as time. There  is only movement in the universe and we compare our own movement to a different object to have a sense of time. It can be a clock or a atomic vibration.  Does this view of time work within the current framework of phsics?  Do physicists have an explanation/proof about time's existence?
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The collapse of the wave function by measurements is one of the most mysterious properties of quantum mechanics.    At what scale does the wave function collapse? What are the conditions for a collapse?  Can it be made precise?  Does the collapse happen instantaneously, or is it spread out in time?  What is the precise equation for the collapse?  Why is the collapse time-asymmetric, and can this explain the arrow of time?
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I was reading some earlier posts on this question in stack exchange. These posts give me the impression that the age of the universe is defined in a certain way following prescriptions such as that:   you should be co moving with the galaxy avoid strong gravitational fields choose the longest proper time recorded in all the frames   Defined this way we get the feeling that the age of the universe is not quite objective. Because we will get a different age if we change the definition. To highlight this arbitrariness, let us consider two space-time travellers A and B equipped with rockets and enough fuel who start at the same space point after setting their respective clocks to zero. Let us say that they started long time ago and took very different space-time paths and meet now and compare their clock readings T(A) and T(B). Each one can in principle claim that his clock showed the age of the universe. One may go a bit further and send a large number of travellers and collect all their clock readings at the end and declare the longest reading as the age of the universe. In this case we can say that the traveller who did not fire his rocket is the winner.  The implication in accepting this definition is that the time shown in this clock is the objective or absolute time of the universe while the times recorded in the other clocks are subjective. This way this definition will bring in a preferred reference frame and make the age of the universe an absolute time and not relative. In relativity theories we have not so far invoked preferred reference frames or absolute time concepts. Should the age of the universe be an exception?     I see that my post has some overlap with some earlier posts.However the important difference is that, as agreed by all who responded to my post,the earlier posts did not indicate that the age of the universe could be as arbitrary as the choice of a reference frame and no reference frame has any privileged status compared to the others.If any one wants to use a particular frame for some reason or another we can not question him.But one can not and should not object to the use of a different frame which computes a much younger universe, say an universe only 2000 years old !!! Lo and Behold! 2000 years can not be true as we know that we existed from much earlier days onwards. Hence the interesting question is: what may be a more realistic lower bound for the age of the universe?
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If we do the wick rotation such that τ = it, then Schrödinger equation, say of a free particle, does have the same form of heat equation. However, it is clear that it admits the wave solution so it is sensible to call it a wave equation.   Whether we should treat it as a wave equation or a heat equation with imaginary time, or both? If it is a wave equation, how do we express it in the form of a wave equation? Is there any physical significance that Schrödinger equation has the same form of a heat equation with imaginary time? For example, what is diffusing?
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OK...before everyone blasts this with references to the relativistic invariance of the physical laws, time dilation, etc let me add some context. Also, I am an amateur with an interest in physics, so I don't know the details of the physics. However, I have read enough about the cosmological principle and cosmic time to develop this "confusion" .  Based on evidence gathered to-date, it appears that the universe is both , as evidenced by observations and the . This principle, when combined with the FLRW metric, allows space-time to be divided into non-intersecting slices and therefore establish a "cosmic time."   Now, the existance of such a time in no way suggests that it is the "right" time or a true "now", hence violating relativity -- although some presentist philosophers (e.g., W.L. Craig) have tried to make this argument, but it is not generally accepted in philosophical circles.  However, this leaves me confused about an apparent disconnect between relativity and the cosmological principle:  Isotropy only holds if we are at rest relative to the cosmic microwave background radiation (universal rest frame), o/w anisotropy is present - yet each reference frame is supposed to allow equally valid observations. How can these two be reconciled when most reference frames would lead us to conclude that the universe is NOT isotropic?  It seems that only by appealing to the idea of being at rest relative to "universal rest frame" can we explain away any discrepancies from isotropy as due to "peculiar motion". However, doesn't this give this "universal rest frame" and its associated time an empirically privileged status, even though physical laws work just fine in every reference frame?   For example (pardon any abuse of astronomy): if look off in some part of space and see only quasars, and then in another part of space and see only brown dwarfs, but I measure both as apparently the same distance from me, then can I conclude that we are in motion, since otherwise we would have an empirical contradiction (kind of like finding dinosaur and human remains in the same strata)?  Any help on where I am going wrong would be helpful. Intuitively, I don't think there should be a way to establish absolute ordering between space-like separated events, but the above reasoning suggests otherwise.
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Is there any mathematical relationship between matter wave (or de Broglie wave) and wave function?  Also, does each type of particle (e.g. photon, electron, positron etc.) have its own unique wave function?
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new finding by Minev et al. seems to suggest that transitions between atomic states are not instantaneous, but continuous processes wherein a superposition smoothly adjusts from favoring one state to another (if I understand it correctly). The authors also claim to be able to catch a system "mid-jump" and reverse it. Popular articles are  and .  I am curious if this finding rules out any interpretations of QM. It seems to generally go against the Copenhagen attitude, which describes measurements as collapsing physical systems into a definite classical state. The popular articles indeed claim that the founders of QM would have been surprised by the new finding.  The link with the asterisk mentions that something called "quantum trajectories theory" predicts what was observed. Is this an interpretation, or a theory? And are they implying that other interpretations/theories don't work?
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I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding.  The Problem:  A Particle sits in an infinite potential well described by  \begin{align} V(x) &amp;= 0, &amp; 0 \leq x \leq L \\ V(x) &amp;= \infty, &amp; \text{otherwise} \end{align}  We know that the energies are given by $E_n = \dfrac{n^2 \pi^2 \hbar^2}{2 m L^2}$ and $\Psi(x) = A_n \sin(n \pi x /L)$.  At time $t_0$ the potential well is suddenly doubled in size, such that the potential is now  \begin{align} V(x) &amp;= 0, &amp; 0 \leq x \leq 2L \\ V(x) &amp;= \infty, &amp; \text{otherwise} \end{align}  So the energies are now given by $\tilde{E}_n = \dfrac{n^2 \pi^2 \hbar^2}{2 \cdot 4 m L^2}$ and $\tilde{\Psi}(x) = \tilde{A}_n \sin(n \pi x /2L)$.   If the particle is in the ground state of the potential well before the change, what is the probability to find the particle in the ground state of the new potential after the change?   This is absolutely clear to me. We find a non vanishing probability as a result. But now it gets tricky:   What is the expectation value of the energy of the particle directly after the change? How does the expectation value of the energy evolve in time?   The solution suggests that the expectation value of the energy does not evolve in time, which is clear to me, since the Hamiltonian is time independent and thus energy is conserved. But it also suggests that the expectation value does not change after we double the width of the potential wall which I understand from the argument of energy conservation but not in terms of quantum mechanics. If the probability that the particle is in the state $\tilde{\Psi}$ does not vanish the particle could have the energy $\tilde{E}_n$ which is lower than $E_n$ and this would mean that the expectation value of energy could change (with a given probability).  What am I missing here, where is my mistake? Any help is appreciated!
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The standard interpretation of $|\psi|^2$ is taken as the probability density of the wave-function collapsing in the given infinitesimal small region. The way this probability is interpreted (at least in the text-book by Griffiths) is that if I prepare a large number of identical states and then perform a measurement on each of them then the probability associated with $|\psi|^2$ actually represents the statistical results of the measurements made (individually) on all these wave-functions of the entire ensemble. This seems like a good enough argument to accept $|\psi|^2$ as the probability density of the wave-function collapsing in a given infinitesimal small region even if I have only one wave-function.  But the  suggests that it is fundamentally impossible to make two states that are completely identical and thus, to my understanding, it makes absolutely no sense to talk about those identical wave-functions that were used to project $|\psi|^2$ as the probability density.  Put in other words, if I can't replicate a wave-function at all then how do I confirm in my laboratory that the probabilities obtained by $|\psi|^2$ actually represents the likely-hood of the collapse happening in a given region?   Edit Is it the catch that the No-Clone Theorem suggests only that a given state can't be evolved to a state identical to another state and it allows the two states being identical if they are so from eternity?
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Added: 5 times down vote for now! Down voter is this religion or physics, please try to explain your decision.  I'm confused about this.  In physics we know for a , but I think that there is a contradiction in this term. The  are the phenomena that  contradicts the vacuum existence because, according to them, the vacuum isn't the empty space.  In vacuum the creation of particle-antiparticle pairs is allowed for small times and this is also proven in practice.  From the other side, the relativistic theory says about space-time that interactions like gravitation bend the vacuum (empty space). There seems to be a contradiction to me. If vacuum is an empty space then we can't bend it, because we can't bend something nonexistent. In other words: we can't bend 'nothing'.  Can empty space really exist in physics?  EDIT1: quote: Luboš Motl     "By definition, the space without   energy is the space whose total value   of energy is equal to 0."   But this space is nonexistent, so it is abstract and should exist only in our mind... Why is so? My second statement of this post says that in physics we cant bend nothing because such a bending is only thinking and not physics!  Another possibility is that space is unknown kind of energy, but this is contradiction in modern physics!  EDIT2:  Can any physics believe that nothing exists? By mathematical logic no! And mathematic is elementary tool in physics. Anything other than that is religion!  Nothing (empty space without energy) is only a logical state!  EDIT3: quote: Roy Simpson:     The General Relativity Vacuum is a   space-time model region without   matter.   and Luboš Motl says: "By definition, the space without energy is the space whose total value of energy is equal to 0."  Agree...   But this is only mathematical Euclidean space + time so this is only a mathematic and not physics! With other words: this is only a method of mathematical mapping. But, in real (not theoretic) physics we can't mapping empty things. Empty is only a logical state!  EDIT4:   Roy Simpsons argumentation seems to me acceptable.   quote: Roy Simpson:     Einstein struggled with this too, and   the problem has come to be known as   the "Hole argument" within GR. You   have to decide whether you are just   interested in GR's vacuum (empty   space) or the full physical vacuum   which includes quantum aspects as   well.   Thanks
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Is this a postulate? I get the expansion of the universe, the addition of discrete bits of space time between me and a distant galaxy, until very distant parts of the universe are moving relative to me, faster than the speed of light. But the other sure seems like  (giant steaming load of convenience) I think I get reasons why, because they don't have any other way to explain the size of the universe and so on. Just seems it would be much easier to  say the universe is eternal and cyclical in nature, and call it a day!