If we know the state of the universe at a certain point in time, is the future set? There have been quite a few similar questions on here and some of the answers were quite useful to me. But there is still some confusion on my part since there seem to be 2 different kinds of answers to this question:   The Schrödinger equation is deterministic. The indeterminism comes from the collapse of the wavefunction when a measurement is made. So the future is not set. A wavefunction only appears to collapse if your quantum system doesn't describe your measuring apparatus as well. A measurement involves entangling the measured system and the measuring system, and in the process simply spreads the coherence from the initial state over both systems. There is no loss of information, it's hard to unentangle the two systems, but theoretically it's possible. So 'knowing the state of the universe at a certain point in time' would be equivalent to knowing the wave function of the universe at a certain point in time, which will then evolve deterministically. So to me this would seem to imply that the future is set.   There have also been some answers saying it depends on the interpretation of quantum mechanics and hence the above question doesn't really have an answer rooted in physics. So my question: Does physics provide an answer to the above question and if so, which of the above answers (if any) is correct?
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I'm not sure if this is the right place to ask this question. I realise that this maybe a borderline philosophical question at this point in time, therefore feel free to close this question if you think that this is a duplicate or inappropriate for this forum. Anyway, I'm an electrical engineer and I have some basic knowledge of quantum mechanics. I know that Schrödinger's equation is deterministic. However, quantum mechanics is much deeper than that and I would like to learn more. If this question is not clearly answerable at this point than can anyone point out some recognized sources that try to answer this question. I would appreciate it if the source is scientific and more specifically, is related to quantum theory.
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It was mentioned to me that it can be shown that there is no classical explanation for the uncertainty in Quantum Mechanics -- i.e. that there are no hidden workings that we have just not yet seen, which could be explained classically and would explain the probabilistic nature of Quantum events in a 'deterministic' fashion.  Can someone explain how this is known please?
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Just watched the 'How Big is the Universe?' TV program and it indicated that the universe is believed to be infinite in size. They used an approach involving measuring the internal angles of triangles. Or something like that anyway.  But hang on, the Universe has a known starting time and size followed by a finite time expanding at a finite speed. So surely, by definition, it cannot be infinite? I can accept it is honking big but by definition it cannot be infinite. Are they misleading me?
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I am doing some research about &quot;time travelling&quot; by shrinking humans to the quantum level. It's something based on the delayed choice quantum experiment, so that we can go back to the past and travel to another parallel universe or to another universe in another timeline. So I just want to make sure if smaller mass changes the way the smaller object experiences time. But do note that I am only 16 so I do wish that it can be simple haha so that I don't end up being more confused.
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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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The many-worlds interpretation of quantum mechanics has always been explained to me at a high level using examples of binary events (e.g. atom either did or did not decay at any given moment in time), which leads to a conceptually clean idea of "branching" into two distinct universes. But how does branching work if you have, say, a 70% probability of something happening (e.g. measuring the spin of an electron having gone through an SG apparatus oriented at an arbitrary angle)?  Do you say that 7 universes got to spin up and 3 that got spin down (to account for the 70% probability)? Does that mean those 7 universes are in-every-way identical copies of each other? But then what if you had something with a 71.87154819...% chance of happening? You would need an uncountably infinite number of branches to be able to represent arbitrarily precise probability ratios, and then subsets of those branches would contain uncountably infinite universes that are 100% degenerate and identical to each other. Is this what the standard many worlds interpretation assumes?  If not this, then what? You can't say that there's a 70% chance of universe A happening and a 30% chance of universe B happening if you're saying both happen. How does the many-worlds interpretation put a "weighting function" on different branches or outcomes?
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I think in quantum mechanics we assign to each system a specific Hilbert space i.e. if systems are different then their Hilbert spaces are different. Is this true? If not why? For differernt system I mean their hamiltonians are different.
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Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?  If so, can quantum mechanics describe the universe at high energies where there is no spacetime?  Schrodinger equation assumes the presence of time dimension. So how can such equations be valid at extremely high energy?  And is it meaningful to do physics if there is no time dimension?  Would the concepts of Hilbert space, wavefunction collapse etc be useful in that case?
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In Lawrence Krauss's book "A Universe From Nothing"; page 62 mentions that for a very short period of time, so small it cannot be measured, an electron due to the uncertainty principle can appear to be moving faster than the speed of light; another way to interpret this is that it's moving back in time.  It further proceeds to say that Feynman used this to suggest that what happens was that an electron and a positron were created, the positron will annihilate with the original electron while the new electron will continue on its merry way.  It finally says that this behavior is confirmed by the spectrum of the Hydrogen atom, among other things.   My question is, how does this not violate special relativity? How is it possible to get an electron moving faster than light? And how did we say it's okay to assume that and simply consider it moving back in time?   (Note, I do not have a degree in Physics so please take that into account while explaining the basic idea).
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What ever happened to  in entangled quantum states, i.e. the ? I thought they argued that in principle one could communicate faster than speed of light with entangled, separated states when one wave function gets collapsed. I imagine this paradox has been resolved, but I don't know the reference.
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I am sorry if this question is silly; it′s just one of those things I wished I asked before leaving university.  If there were a static universe only as big as the size of two particles, say electrons, and there were one electron in it going back and forth from point A to point B: would time also go back and forth in the future (point B) and in the past (point A), or would it be considered to  go forward as it does for us? would it be possible to know how long that electron stayed at point A or point B, would it even make sense to ask? I guess what I am asking is: does time move forward only because there are so many particles moving in this enormous space that it is almost impossible they would all be back in the same position they held at least once before relative to each other? does time exist only as a consequence of a lot of particles and their position relative to each other, and the space for them, just like heat?
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I was browsing through Foundations of Space and Time, a compilation of essays on various theories of quantum gravity. The following passage in the introduction intrigued me:     Each compactification leads to a different vacuum state.... at least one state should describe our Universe in its entirety.... the enormous number (~10^500 at last count) of solutions, with no perturbative mechanism to select mechanism to select among them, leads some critics to question the predictive power of the theory..Even more worrying is that, while the theory is perturbatively finite order by order, the perturbation series does not seem to converge.   I don't know anything about string theory and so I could not make head or tails this. All I know is that ~$10^{500}$    is a very large number.    What exactly is a 'solution' in string theory? Is it a spacetime metric of some sort or the terms of a S-matrix of some sort?   Why are there so many 'solutions'?  I thought string theory was supposed to be finite, why do perturbative series still diverge? Is there any experimental technique to limit the number of 'solutions'?   Will experimental techniques be able to pinpoint a solution within present day string theorists' lifetimes too? If not, how long will it take before we can experimentally probe these things?  Are string theorists completely relaxed about these issues? Or are they in anguish?
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Possible Duplicate:             As asked in the title, can a Universe which is deterministic at its fundamental level still allow free will?
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I'm new here, so apologies if the question doesn't sound meaningful considering what physics is supposed to answer. I don't have a physics or mathematics background, but I did learn a few things about entropy and the different possible fates of an expanding universe from other forums.   Now, assuming the heat death "fate" is where the universe is heading towards, asymptotically reaching towards a thermal equilibrium, will it stay in a state of equilibrium forever? or the will the "arrow of time" cease pointing sharply towards the future since decrease in entropy becomes likelier when a state of near maximal entropy is achieved (I'm guessing here) ?  The wiki article on this states the number of years that would take for a random quantum fluctuation to perhaps recreate another "big bang" and restart the universe as $10^{10^{10^{56 }}}$ . I realise that's a RIDICULOUS amount of time to even comprehend, nevertheless it is still a physical possibility and $10^{10^{10^{56}} }$ years are only a tiny fraction of time when compared to an infinite amount of time.  Finally what I want to ask: Is reality a one time phase transition from a vague potential with maximal degrees of freedom (big bang) to a crisp actuality with maximal constraint (heat death) with asymmetric, unidirectional time or is it infinite cyclic with symmetric time that reverses itself (by means of highly improbable, but physically not impossible mechanisms) after a finite period of time?   I suspect this may be a borderline philosophy question, but figured might as well give it a try here before posting in more relevant forums. Thanks.
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In the  for quantum mechanics, the first postulate states that a quantum state is a vector in a separable Hilbert space. It means it is assumed the Hilbert space has a basis with at most infinite countable elements (cardinality). In other words, it states that the energy of an arbitrary system is discrete. Is it always true? If not, can you make an specific example in nature that its eigen-energies are uncountable?
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I was looking at a website that claims to generate random numbers from observation of quantum effects. This lead me to question how we know that the numbers are truly random.  When we observe a probability wave and it collapses in one place into a particle, how do we know that the location of the particle is really random?  Do we have any evidence of the randomness, or is it just that no one can predict the location right now?
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I'd appreciate a bit of clarification on how conservation of energy works in QM.  The infinite square well has a set of stationary states, each corresponding to one of the discrete energy levels of the well. A particle in a particular state can be represented as a sum of these stationary states. The expectation value of the Hamiltonian, &lt; H &gt; , of this particle does not change with time. The state however (by virtue of being a sum of multiple stationary states) has a non-zero energy-uncertainty.  Measuring the energy of the particle collapeses its wavefunction into one of the stationary states with a corresponding energy value.  This bothers me. While  &lt; H &gt;  is constant, the "actual" energy of the particle (upon measurement) could vary greatly. This seems like a violation of energy conservation. [And while I've posited this question in terms of the infinite well, any wavefunction composed of non-degenerate stationary states seems like a violation to me]  So, is the particle entangled with some other particle (through whatever process put it in the well in the first place) such that the net energy in some larger system is constant? Or is energy only conserved is larger systems (which are compromised of so many particles as to approach  &lt; H &gt; )? Or what am I misunderstanding?