Nonlocal Wave Function Research Articles

Quantum physics and biology: the local wavefunction approach

Is there a single linearly evolving Wave Function of the Universe that is able to lead to all the nonlinearities we see around us? This proposal seems a priori highly implausible. I claim that instead, in the real Universe, generically only local wave functions exist. Non-local wave functions occur for carefully engineered contexts such as Bell experiments, but there is no single wave function for a cat or macroscopic object such as a brain, let alone for the Universe as a whole. Contextual wave function collapse leads to a defensible version of the Copenhagen interpretation of quantum theory, where classical macro levels provide the context for quantum events and biological emergence. Complexity arises via multiscale adaptive modular hierarchical structures that enable logical branching to emerge from the underlying linear physics. Each emergent level is causally effective because of the meshing of upwards and downwards causation that takes place consistently with that physics. Quantum chemistry approaches in biological contexts fit this local wavefunction picture.

Direct Measurement of a Nonlocal Entangled Quantum State.

Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen etal. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.

High-Frequency Electromagnetic Emission from Non-Local Wavefunctions

In systems with non-local potentials or other kinds of non-locality, the Landauer-Büttiker formula of quantum transport leads to replacing the usual gauge-invariant current density J with a current J e x t which has a non-local part and coincides with the current of the extended Aharonov-Bohm electrodynamics. It follows that the electromagnetic field generated by this current can have some peculiar properties and in particular the electric field of an oscillating dipole can have a long-range longitudinal component. The calculation is complex because it requires the evaluation of double-retarded integrals. We report the outcome of some numerical integrations with specific parameters for the source: dipole length ∼10−7 cm, frequency 10 GHz. The resulting longitudinal field E L turns out to be of the order of 10 2 to 10 3 times larger than the transverse component (only for the non-local part of the current). Possible applications concern the radiation field generated by Josephson tunnelling in thick superconductor-normal-superconductor (SNS) junctions in yttrium barium oxide (YBCO) and by current flow in molecular nanodevices.

Design of a test for the electromagnetic coupling of non-local wavefunctions

It has recently been proven that certain effective wavefunctions in fractional quantum mechanics and condensed matter do not have a locally conserved current; as a consequence, their coupling to the electromagnetic field leads to extended Maxwell equations, featuring non-local, formally simple additional source terms. Solving these equations in general form or finding analytical approximations is a formidable task, but numerical solutions can be obtained by performing some bulky double-retarded integrals. We focus on concrete experimental situations which may allow to detect an anomalous quasi-static magnetic field generated by these (collective) wavefunctions in cuprate superconductors. We compute the spatial dependence of the field and its amplitude as a function of microscopic parameters including the fraction $\eta$ of supercurrent that is not locally conserved in Josephson junctions between grains, the thickness $a$ of the junctions and the size $\varepsilon$ of their current sinks and sources. The results show that the anomalous field is actually detectable at the macroscopic level with sensitive experiments, and can be important at the microscopic level because of virtual charge effects typical of the extended Maxwell equations.

Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements.

A single quantum particle can be described by a wavefunction that spreads over arbitrarily large distances; however, it is never detected in two (or more) places. This strange phenomenon is explained in the quantum theory by what Einstein repudiated as 'spooky action at a distance': the instantaneous nonlocal collapse of the wavefunction to wherever the particle is detected. Here we demonstrate this single-particle spooky action, with no efficiency loophole, by splitting a single photon between two laboratories and experimentally testing whether the choice of measurement in one laboratory really causes a change in the local quantum state in the other laboratory. To this end, we use homodyne measurements with six different measurement settings and quantitatively verify Einstein's spooky action by violating an Einstein-Podolsky-Rosen-steering inequality by 0.042±0.006. Our experiment also verifies the entanglement of the split single photon even when one side is untrusted.

On the uncertainty of the ordering of nonlocal wavefunction collapse when relativity is considered

The temporal measurement order and therefore the originator of the instantaneous collapse of the wavefunction of a spatiality entangled particle pair can change depending on the reference frame of an observer. This can lead to a paradox in which its seems that both measurements collapsed the wavefunction before the other. We resolve this paradox by demonstrating how attempting to determine the order of measurement of the entangled pair introduces uncertainty which makes the measurement order impossible to know.

Evidence of nonlocality due to a gradient term in the optical model

We demonstrate that the presence of a velocity-dependent term in the phenomenological optical potential simulates a source of nonlocality. This is achieved by showing that, in the interior of the nucleus, the nonlocal wave functions are different from the corresponding local ones obtained in the absence of the velocity-dependent term in accordance with the Perey effect. It is also shown that the enhancement or suppression of the nonlocal wave function is energy as well as angular momentum dependent. The latter is in line with the results of previous works that introduced parity dependent terms in the conventional optical potential.

Observation of Two-Source Interference in the Photoproduction ReactionAuAu→AuAuρ0

In ultraperipheral relativistic heavy-ion collisions, a photon from the electromagnetic field of one nucleus can fluctuate to a quark-antiquark pair and scatter from the other nucleus, emerging as a rho{0}. The rho{0} production occurs in two well-separated (median impact parameters of 20 and 40 F for the cases considered here) nuclei, so the system forms a two-source interferometer. At low transverse momenta, the two amplitudes interfere destructively, suppressing rho{0} production. Since the rho{0} decays before the production amplitudes from the two sources can overlap, the two-pion system can only be described with an entangled nonlocal wave function, and is thus an example of the Einstein-Podolsky-Rosen paradox. We observe this suppression in 200 GeV per nucleon-pair gold-gold collisions. The interference is 87%+/-5%(stat.)+/-8%(syst.) of the expected level. This translates into a limit on decoherence due to wave function collapse or other factors of 23% at the 90% confidence level.

An amusing analogy: modelling quantum-type behaviours with wormhole-based time travel

When backward time travel through wormholes is taken into account, classical physics loses its determinism and allows simulation of some quantum behaviours. We show how it is possible to simulate a non-local wavefunction reduction-type effect, i.e. we present a mechanical analogy for the collapse of the wavefunction of an entangled state of two removed particles. This situation can be seen as the simplest EPR situation, i.e. the situation where there is just one direction to measure along the spin (or the correlated properties). We present no rigorous results here, just a different point of view about something that is generally thought to be impossible: modelling a quantum indeterministic and non-local behaviour with a mechanical system.

Comparison of several equivalent local potentials for microscopic nonlocal Nα potentials

The phase shifts obtained in the Perey-Saxon, Horiuchi and Peierls-Vinh Mau approximations for the microscopic nonlocal Nα interaction of Lassaut and Vinh Mau have been compared at 10 and 20 MeV to the exact results, without the customary approximation of Perey and Buck, which neglects part of the angular dependence of the nonlocality and is inadequate. We have also compared the equivalent local potentials with the corresponding local wave functions and damping factors to their exact wronskian counterparts and obtained the corresponding nonlocal wave functions as a product of the approximate local wave function and the damping factor in all cases. The results show that of all the approximations the Peierls-Vinh Mau approximation is the most accurate one for s-waves and that the Perey-Saxon approximation is inadequate for Nα scattering. The accuracy of all the approximations is dependent on the degree of repulsiveness of the effective nuclear force. For the exact wronskian equivalent local potential and damping factor however, we reproduce the exact nonlocal wave function to high accuracy in all cases, confirming the accuracy of our numerical methods. The implications for nuclear reactions where the off-shell behaviour of the Nα interaction is important are discussed.

Complex local equivalents to imaginary non-local potentials: Neutron scattering from 208Pb

The complex equivalent local potential to an imaginary non-local potential obtained in a weak coupling particle vibration model for low energy s-wave neutron elastic scattering from 208Pb is presented. The local potential contains a non-zero real part, is surface peaked, and exhibits resonances. The equivalent local potential and damping of the local wave function relative to the non-local wave function depend on the strength of the Woods-Saxon real central potential also present in the Schroedinger equation.

Single-particle states in non-local potentials and direct nuclear reactions

The non-local model of Perey and Buck is extended to the bound-state problem. For 16O and 40Ca, the single-particle states in the non-local potential are compared with those in a local Woods-Saxon potential and with experiment. Different approximations for the non-local wave functions of bound and scattering states are tested and found to be very useful. The influence of the non-locality in zero-range DWBA calculations of the 16O(d, p) 17O and 18O(p, p′) reactions is investigated. For the stripping reaction the differential cross sections are compared with those obtained using a sharp radial cut-off.

The equivalent local potential and the Perey effect

The equivalent local potential and the reduction factor for the non-local wave function compared to the equivalent local wave function inside the nucleus are calculated in the Perey-Saxon approximation in such a way that the wave function does not appear explicitly in the formulae obtained. The equivalent local potential and the reduction factor only depend on the equivalent local potential of Perey and Buck. The result is in good agreement with Perey's numerical comparisons.