Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHow the instant collapse of a spatially-extended quantum state is consistent with relativity of simultaneity
149
0
0.0
(
0
)
Authors
Moses Fayngold
Ask ChatGPT about the research
No Arabic abstract
A thought experiment is considered on observation of instantaneous collapse of an extended wave packet. According to relativity of simultaneity, such a collapse being instantaneous in some reference frame must be a lasting process in other frames. But according to quantum mechanics, collapse is instantaneous in any frame. Mathematical structure of quantum mechanics eliminates any contradictions between these two apparently conflicting statements. Here the invariance of quantum-mechanical collapse is shown to follow directly from the Born postulate, without any use of mathematical properties of quantum operators. The consistency of quantum mechanics with Relativity is also shown for instant disentanglement of a composite system.
rate research
Read More
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian background is presented as an intrinsic fundamental classical presumption. However, the Hamiltonian formulation of classical analytical mechanics is based on abstract generalized coordinates and momenta: It is a mathematical rather than a philosophical framework. If the metaphysical assumptions ascribed to classical mechanics are dropped, then there exists a presentation in which little of the purported difference between quantum and classical mechanics remains. This presentation allows to derive the mathematics of relativistic quantum mechanics on the basis of a purely classical Hamiltonian phase space picture. It is shown that a spatio-temporal description is not a condition for but a consequence of objectivity. It requires no postulates. This is achieved by evading spatial notions and assuming nothing but time translation invariance.
In this work we consider some consequences of the Bohr-Sommerfeld-Hansson (Old or quasi-classical) quantum theory of the Newtonian gravity, i.e. of the gravitational atom. We prove that in this case (for gravitational central force and quantized angular momentum) centrifugal acceleration becomes formally-theoretically dependent (proportional to fourth degree) of the mass of gravitational electron rotating around gravitational nucleus for any quantum number (state). It seemingly leads toward a paradoxical breaking of the relativistic equivalence principle which contradicts to real experimental data. We demonstrate that this equivalence principle breaking does not really appear in the (quasi classical) quantum theory, but that it necessary appears only in a hypothetical extension of the quantum theory that needs a classical like interpretation of the Bohr-Sommerfeld angular momentum quantization postulate. It is, in some sense, similar to Bell-Aspect analysis that points out that a hypothetical deterministic extension of the quantum mechanics, in distinction to usual quantum mechanics, can reproduce experimental data if and only if it is non-local (superluminal) in contradiction with relativistic locality (luminality) principle.
We elaborate on a geometric characterization of the electromagnetic properties of matter. A fundamental complex quantity, z_{L}, is introduced to study the localization properties of extended quantum systems. z_L, which allows us to discriminate between conducting and non-conducting thermodynamic phases, has an illuminating physical (and geometric) interpretation. Its phase can be related to the expectation value of the position operator (and a Berry phase), while its modulus is associated with quantum electric polarization fluctuations (and a quantum metric). We also study the scaling behavior of z_L in the one-dimensional repulsive Hubbard model.
This work addresses two problems in the context of two-party communication complexity of functions. First, it concludes the line of research, which can be viewed as demonstrating qualitative advantage of quantum communication in the three most common communication layouts: two-way interactive communication; one-way communication; simultaneous message passing (SMP). We demonstrate a functional problem, whose communication complexity is $O((log n)^2)$ in the quantum version of SMP and $tildeOmega(sqrt n)$ in the classical (randomised) version of SMP. Second, this work contributes to understanding the power of the weakest commonly studied regime of quantum communication $-$ SMP with quantum messages and without shared randomness (the latter restriction can be viewed as a somewhat artificial way of making the quantum model as weak as possible). Our function has an efficient solution in this regime as well, which means that even lacking shared randomness, quantum SMP can be exponentially stronger than its classical counterpart with shared randomness.
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation returns to Schrodinger integral equation. When N becomes sufficiently large, it is equivalent to Einstein field equation. This illustrates formal unification and intrinsic compatibility of general relativity with quantum mechanics. The quantum gravity equation may be utilized to deduce general relativity, special relativity, Newtonian mechanics and quantum mechanics, which has paved the way for unification of theoretical physics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
