An Eotvos experiment to include paramagnetic effects?
Galileo considered the necessary equivalent rate of acceleration of a rubix cube of material not in "contact" versus a "whole" cube of the same material (as such slightly denser) falling in a gravitational field. His conclusion was that because the constituent cubes must all fall at g=9.81ms^-2 just as the whole cube then g is universal for all bodies immersed in the field regardless of their mass (indeed density).
Image credit: (weisshouse.com). See discussion googlePlus-science on what is contact.
Eotvos has affirmed the indifference of the gravitational field to the materiality of a body freely falling through to one part in 10^17. Two test masses effectively follow the same geodesic as long as they have the same bulk mass; the precise make-up of the constituent stuff bound as they are by differing electrostatic and nuclear forces is irrelevant to the external acceleration field. One may ask whether it is useful to augment the Eotvos experiment by choosing one material that possesses an additional bulk property of paramagnetism.
A quantum equivalent of Maxwell's displacement ("current") field should add drag even though the quantum electrodynamic vaccuum that it is falling though is electrically neutral. Would a ferromagnet decelerate while falling through free-space (permeated only by a uniform gravitational field) more than a non-ferrous metal due to the retarding action described by Lenz's law as the creation of "eddy-displacement fields" in the "dielectric" of the (quantum electrodynamic) vacuum resist its fall?
To answer this we will have to consider the standard Eotvos experiments that look to confirm the degree to which the so-called Weak Equivalence Principle of Einstein applies across matter types and the nature of the displacement ("current") field in Ampere's Law. First, lets make reference to Maxwell's equations in describing the classic demonstration of Lenz's law and the appearance of his mysteriously misnamed "displacement current".
and observing its rate of descent as slower than if a non-magnet metal the same size was dropped. The movement of circulating magnet flux lines during the magnet's descent induces a displacement field through the copper tube. According to Maxwell-Lorentz-Einstein electrodynamics this bona fide electric field then accelerates the free electrons in the copper tubing creating an "eddy' current in the copper. The magnetic part of the Lorentz force, F=qE + qvB associated to the movement of electric charge induces a Magnetic force that acts in the opposite direction to the gravitational force thus slowing its descent according to what is called "Lenz's law". Without a conducting material you just have a latent time varying Electric field.
The name given to the field of "displacement current" is a misnomer as it is an electric current only when there are moving charges. It is not the J in Ampere's law but the dD/dt. Without a conductor for a tube (or indeed some dielectric material) the displacement field exists.
The induced electric field (just as with a "normal" displaced electric charge induced electric field) in the presence of a copper conductor (with its free electrons) enables an "induced current" to flow. This induced electric field is there whether or not there is a conductor present though, just as the gravitational field is there whether there is test matter to freely fall in it. Below are Maxwell's equations using Helmholtz divergence and curl notation.
You read the "point form" as right hand side is source of left. But as with any equality it goes both ways! So that the latter two divergence laws (Nabla dot) mirror Newtonian gravity's inverse square law (from a massive point source). That is, they can all be described by Laplace's equation for a scalar potential field that falls off as 1/r.
For Maxwell, instead of the bulk gravitational mass quality of matter generating a potential that gives rise to a conservative (path independent) force, in his equations the surface electric and magnetic (monopole) charges are the sources.
D is the "displacement" current that Maxwell added to give the equations full symmetry in space and time and J is an electric current source which we don't have in our copper tube so the Eddy current is the time changing D. Curl H (Nabla cross) is the circulating Magnetic field source. A picture used in the context of polarization modes imprinted on the CMBR sums up the difference in the divergence and circulatory properties of the Divergence and Curl operations.
Typically, because no magnetic monopoles have been discovered the Electric field is traditionally defined by Gauss's law with its potential field diverging (E Mode) from a point (at least spherical) source and magnetic dipoles to the circulatory field ("B mode') lines.
Magnetic fields can though, as Faraday's Law shows us can be generated from a circulating (centripetally accelerating) electric current.
One might as why this Magnetic sourced current is not called a "circulation current". It is described by the Ampere's law of Maxwell's four equations and shows that the Eddy current is sourced from a circulatory Magnetic field, H (note use of the Helmholtz's "Curl" notation "Nabla x", an axial rotating tangential vector field!). On the etymology even Maxwell believed in an mechanical (aether-based) mechanism for the propagation of his light in a vacuum of intertwining electric and magnetic fields.
Within the fluid dynamics community there is little difference between the terms "vortex" and an "eddy" just their contextual usage. That is within turbulence in all fluid types, be they liquids, gases or plasma you usually speak of eddies with these eddies decaying into to smaller eddies to form a turbulent cascade. Vortices are deemed more stable structures and the description of their physics (e.g. geostrophic winds) does not necessarily include the formation of turbulent cascades.
Either way the eddy or vortex currents in the copper tube if the etymology is correct should not exhibited laminar (continuous non crossing field) flow characteristics. So does our solid conducting metal tube carrying circulating charges driven by a displacement field constitute the name an eddy flow? The argument goes that we have a "cascade of ever more smaller self-similar eddy currents circulating in the copper tube when a magnet is dropped down inside it. Maxwell tells us that as an eddy current flows a secondary magnetic field is generated which would then create a secondary eddy current, a tertiary magnetic field...
If somehow there is thermal dissipation of energy that makes this an energy dissipating cascade what then would be the case if the tube was a superconductor? No cascading eddies then? Then that induced current would be just a plain old circulatory current?
composition, fall with precisely the same acceleration.
The principle asserts the exact identity of inertial mass mi (the mass appearing in Newton’s second law) and gravitational mass mg (the mass appearing in Newton’s law of gravity).
This was the first great unification program of Newton, relating the dynamics of the Heavens to the inertial trajectories of earth bound objects.
The presumption of Equivalence of inertial and gravitational masses was subsequently unpicked by Einstein in formulating his Equivalence principle of which his elevator experiments encapsulate his thinking nicely if not fully.
eotvos latest
A quantum equivalent of Maxwell's displacement ("current") field should add drag even though the quantum electrodynamic vaccuum that it is falling though is electrically neutral. Would a ferromagnet decelerate while falling through free-space (permeated only by a uniform gravitational field) more than a non-ferrous metal due to the retarding action described by Lenz's law as the creation of "eddy-displacement fields" in the "dielectric" of the (quantum electrodynamic) vacuum resist its fall?
To answer this we will have to consider the standard Eotvos experiments that look to confirm the degree to which the so-called Weak Equivalence Principle of Einstein applies across matter types and the nature of the displacement ("current") field in Ampere's Law. First, lets make reference to Maxwell's equations in describing the classic demonstration of Lenz's law and the appearance of his mysteriously misnamed "displacement current".
Maxwell's "Displacement field" and Lenz's Law
A popular high school demonstration is that of dropping a neodymium magnet through a (conducting but non -significantly-ferromagnetic) tubeThe name given to the field of "displacement current" is a misnomer as it is an electric current only when there are moving charges. It is not the J in Ampere's law but the dD/dt. Without a conductor for a tube (or indeed some dielectric material) the displacement field exists.
The induced electric field (just as with a "normal" displaced electric charge induced electric field) in the presence of a copper conductor (with its free electrons) enables an "induced current" to flow. This induced electric field is there whether or not there is a conductor present though, just as the gravitational field is there whether there is test matter to freely fall in it. Below are Maxwell's equations using Helmholtz divergence and curl notation.
You read the "point form" as right hand side is source of left. But as with any equality it goes both ways! So that the latter two divergence laws (Nabla dot) mirror Newtonian gravity's inverse square law (from a massive point source). That is, they can all be described by Laplace's equation for a scalar potential field that falls off as 1/r.
For Maxwell, instead of the bulk gravitational mass quality of matter generating a potential that gives rise to a conservative (path independent) force, in his equations the surface electric and magnetic (monopole) charges are the sources.
D is the "displacement" current that Maxwell added to give the equations full symmetry in space and time and J is an electric current source which we don't have in our copper tube so the Eddy current is the time changing D. Curl H (Nabla cross) is the circulating Magnetic field source. A picture used in the context of polarization modes imprinted on the CMBR sums up the difference in the divergence and circulatory properties of the Divergence and Curl operations.Typically, because no magnetic monopoles have been discovered the Electric field is traditionally defined by Gauss's law with its potential field diverging (E Mode) from a point (at least spherical) source and magnetic dipoles to the circulatory field ("B mode') lines.
Magnetic fields can though, as Faraday's Law shows us can be generated from a circulating (centripetally accelerating) electric current.
Eddy, Vortex or Circulating Current?
One might as why this Magnetic sourced current is not called a "circulation current". It is described by the Ampere's law of Maxwell's four equations and shows that the Eddy current is sourced from a circulatory Magnetic field, H (note use of the Helmholtz's "Curl" notation "Nabla x", an axial rotating tangential vector field!). On the etymology even Maxwell believed in an mechanical (aether-based) mechanism for the propagation of his light in a vacuum of intertwining electric and magnetic fields.
Within the fluid dynamics community there is little difference between the terms "vortex" and an "eddy" just their contextual usage. That is within turbulence in all fluid types, be they liquids, gases or plasma you usually speak of eddies with these eddies decaying into to smaller eddies to form a turbulent cascade. Vortices are deemed more stable structures and the description of their physics (e.g. geostrophic winds) does not necessarily include the formation of turbulent cascades.
Superconducting Eddy Currents
Either way the eddy or vortex currents in the copper tube if the etymology is correct should not exhibited laminar (continuous non crossing field) flow characteristics. So does our solid conducting metal tube carrying circulating charges driven by a displacement field constitute the name an eddy flow? The argument goes that we have a "cascade of ever more smaller self-similar eddy currents circulating in the copper tube when a magnet is dropped down inside it. Maxwell tells us that as an eddy current flows a secondary magnetic field is generated which would then create a secondary eddy current, a tertiary magnetic field...
If somehow there is thermal dissipation of energy that makes this an energy dissipating cascade what then would be the case if the tube was a superconductor? No cascading eddies then? Then that induced current would be just a plain old circulatory current?
Eotvos and the Weak Equivalence Principle
The weak equivalence principle (WEP) states that in a uniform gravitational field all objects, regardless of their
composition, fall with precisely the same acceleration.The principle asserts the exact identity of inertial mass mi (the mass appearing in Newton’s second law) and gravitational mass mg (the mass appearing in Newton’s law of gravity).
This was the first great unification program of Newton, relating the dynamics of the Heavens to the inertial trajectories of earth bound objects.
The presumption of Equivalence of inertial and gravitational masses was subsequently unpicked by Einstein in formulating his Equivalence principle of which his elevator experiments encapsulate his thinking nicely if not fully.
eotvos latest
Note that WEP implicitly assumes that the falling objects are bound by non gravitational (Nuclear-Yukawa type binding) forces. Departures from the exact equality of mg/mi for objects 1 and 2 as specified by the Eotvos parameter have not been detected to orders of 1 in 10^17
η1,2 = a1 − a2 = (mg/mi)1 − (mg/mi)2 , (1) (a1 + a2)/2 [(mg/mi)1 + (mg/mi)2 ]/2
Our question then can be framed as to whether there is an equivalent Eotvos experiment for magnetic (ferromagnetic) versus non magnetic materials falling through an effective vaccuum dielectric?
Its effects would either mask or be masked by the different materiality of the freely falling bodies as captured in a pure Eotvos experiment.
To get a feel for the possible quantum effects that would have to be considered in motivating better such an experiment (our consideration to date have been classical). The related perhaps unobserved Unruh and observed Casimir effects are two phenemena that are predicted by the virtual particle froth that emmanates from the quantum electrodynamic vacuum.
The Unruh effect is the prediction that an accelerating observer will observe blackbody radiation where an inertial observer would observe none. The vacuum background appears to be warm from an accelerating reference frame so a thermometer waved around in empty space will (by virtue of its accelerated motion) record a non-zero temperature. wiki Unruh effect
Consider finally layers of graphene separated by a little more than their van der Waals bond length of 0.3nm. "Not in contact" That is, they have the electrical conductivity properties of graphene (graphineReview) sheets and not graphite.
η1,2 = a1 − a2 = (mg/mi)1 − (mg/mi)2 , (1) (a1 + a2)/2 [(mg/mi)1 + (mg/mi)2 ]/2
Our question then can be framed as to whether there is an equivalent Eotvos experiment for magnetic (ferromagnetic) versus non magnetic materials falling through an effective vaccuum dielectric?
Its effects would either mask or be masked by the different materiality of the freely falling bodies as captured in a pure Eotvos experiment.
To get a feel for the possible quantum effects that would have to be considered in motivating better such an experiment (our consideration to date have been classical). The related perhaps unobserved Unruh and observed Casimir effects are two phenemena that are predicted by the virtual particle froth that emmanates from the quantum electrodynamic vacuum.
Unruh effect
Casimir Effect
When two uncharged objects are placed in a vacuum with no external fields, we wouldn't expect them to have any force between them other than gravity. Quantum electrodynamics says otherwise. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the quantum electrodynamic vacuum, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force– either an attraction or a repulsion depending on the specific arrangement of the two plates.Multi Graphene-layered Detector
Consider finally layers of graphene separated by a little more than their van der Waals bond length of 0.3nm. "Not in contact" That is, they have the electrical conductivity properties of graphene (graphineReview) sheets and not graphite.
If suitably separated vertically parallel sheets are dropped in a gravitational field they will at some point become graphite pulled in by tidal forces of the gravitational field. If rather separated horizontally they will separate further on falling, becoming more distended in their sheet formation.
As such the respective electrical properties of the two configurations will be different depending on "point of contact" reached through orientation in the external field. So random question/thoughts:
1-Is there some version of the strong equivalence principle that could be usefully investigated (an Eotvos experiment) here?
2-could one envision a Lenz law induced differential acceleration across the two orientations: eddy currents decelerating the material vertically aligned greater than horizontally by Faraday's law?
Given that graphene is a thin layer allotrope of pure carbon 12 ("in the structure of a plane of sp2 bonded atoms with a molecule bond length of 0.142 nm") one could consider a more traditional Eotvos in which an alternative set of graphene sheets doped with greater percentage of isotopes of carbon 13: arxiv.org - arxiv.org/pdf/1112.5752.pdf
as such denser are also dropped.
This would confirm the acceleration dependence, given density difference and materiality of object of free fall.
As such the respective electrical properties of the two configurations will be different depending on "point of contact" reached through orientation in the external field. So random question/thoughts:
1-Is there some version of the strong equivalence principle that could be usefully investigated (an Eotvos experiment) here?
2-could one envision a Lenz law induced differential acceleration across the two orientations: eddy currents decelerating the material vertically aligned greater than horizontally by Faraday's law?
Given that graphene is a thin layer allotrope of pure carbon 12 ("in the structure of a plane of sp2 bonded atoms with a molecule bond length of 0.142 nm") one could consider a more traditional Eotvos in which an alternative set of graphene sheets doped with greater percentage of isotopes of carbon 13: arxiv.org - arxiv.org/pdf/1112.5752.pdf
as such denser are also dropped.
This would confirm the acceleration dependence, given density difference and materiality of object of free fall.
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