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Practical Applications ofWeber Force

byKjell Prytz

University of MalardalenVasteras, SwedenKjell.Prytz@mdh.se

Beyond Relativity?Consistent with Relativity but:• No Space-time• No Fields• Force Perspective

2Start 2:50

C Source of InertiaStart 2:40

B Meissner Effect

Start 0:50

A Magnetic Force

Weber Force in Practice

• Heuristic derivation of Weber force

• Speed in electrodynamics – the observer

• A Liverpool experiment – Verify Weber force

• B Meissner Effect – Apply Weber force in electromagnetism

• Electrodynamic and Gravitational Force Formulas

• Origin of Inductance – ElectromagneticInertia

• C Origin of Inertia – Apply Weber force in gravitation 3

Weber Force in Practice - Content

Origin of magnetism

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2 2

0 02 2

0 0

ˆ( ')4 4

e mf F F

q qvv R

R R

0 0

1c

Speed of light

Force f on right charge

Parallel current-carryingconductors

Conduction electrons Pair of electrons

Fe is electric force

Fm is magnetic force

5

Derivation of magnetism and speed of light

where w is speed of propagation

so that w is speed of light0 0

1w c

Origin of induction – Weber Force

6Weber’s acceleration dependent forceForce on object 2

Relative Motion - meaning of speed and observer

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Relative rest – only electric force

Relative speed v – electric and magnetic force

Relative speed v – electric and magnetic force

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Accelerator Example – Bennet Pinch

https://books.google.se/books?id=v9SoaCWFgigC&pg=PA531&lpg=PA531&dq=repulsive+force+in+accelerators&source=bl&ots=DzmeGCUgD1&sig=ACfU3U03dkbGYJRkGxGhYZES6Em2-GR5hQ&hl=sv&sa=X&ved=2ahUKEwjF0ZbP2KXkAhXyo4sKHarND344FBDoATABegQICRAB#v=onepage&q=repulsive%20force%20in%20accelerators&f=false

https://www.plasma-universe.com/pinch/

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2 2

2 2

0

(1 )4

q vf

R c

At speed of light relative the observer, the force betweenthe charges vanishes, although their relative velocity is zero.

(Newtonian force)

Bennet Pinch simplified

Liverpool Experiment – Verification of Weber ForceSmith, Jjunju and Maher

Lorentz – steady current in solenoidWeber – charges accelerate centripetally

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https://www.youtube.com/watch?v=jtiJveZVRPU

Meissner Effect

11Starts at 2:40

Meissner Effect – explained classically by Weber force

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Coil carrying current I is placed on a superconducting material. Charge carriers of the coil are acceleratedcentripetally

Charge carriers ofthe material respond with a force oppositely directedto the centripetal force

Since the material is influenced by a magneticfield, the Lorentz force generates a circulatingcurrent in the oppositedirection

Blue line – ”Magnetic Field”Red lines – Electric current

As in Liverpool Experiment, the centripetal acceleration is crucial(neglected in Maxwell theory)

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V V

Observer at rest

Observer in motion

V

Relative rest

Pairwise interaction between identical objects

V V

Observer at rest

Observer in motion

V

Relative rest

Arrows in red are the magnetic effects, i.e. motional effects

Electromagnetism Gravitation

Electrodynamics vs Gravitation – Origin of Inertia

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Assuming interaction speed is c and is invariant for bothgravitation and electromagnetism, similar motional effectsoccur in gravitation as in electrodynamics

This force is the origin ofinertial mass

RR

mmGfg

ˆ2

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Electrodynamics Gravitation (General Relativity)

Rest

Uniform motion

Acceler-ation

RR

qqfe

ˆ4 2

0

21

Rc

v

R

qqfem

ˆ14

12

2

2

21

0

dt

vd

Rc

qqf ind

1

2

0

21

4

2

1 2

2 2ˆ4 1gm

m m vf G R

R c

1 2 1

24g ind

m m dvf G

c R dt

This force is the origin ofinductance

Gravitational Inductive Force and Inertial Mass

Sciama 1952 (no factor 4)

Mach’sprinciple

Electromagnetic Inertia - Inductance

Simplest case LR circuit –’self inductance’ of coil

•When connected to voltage, velocity of electronsincreases exponentially. They exhibit inertia to acceleration.

•Its origin is the interaction with the rest of the charges in the universe, but primarily due to thosein the conductor.

•An object with gravitational interaction exhibits similar kind of effect.

•Instead of inductance we call this property inertial mass.

L

DF

R

Current

Time

Mach’sprinciple1893

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Generation of Current

Direction ofconduction electrons

Current direction

+

-

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finda find

a

finda

finda

finda

finda

finda

During acceleration

All electrons accelerate in same direction

Each electron experiences the collectiveeffect from all the other electrons

The inductive force find is the origin ofinductance (also source of magnetic energy)

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Gravitational Inductive Force

In the frame of a stationaryobserver

In the rest frame of m2

Gravitational induction force is in the same direction as the acceleration of the influence (to the contrary ofelectrodynamics)r

Gravitational masses

te is emission time(retarded time)

t0 is observation time

V is universe volume

r is mass density

Using cosmological model LCDM (Big Bang, Dark Matter, Dark Energy, Isotropic)

2 2(1.15 0.15)inertm m

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Total inductive force on m2 obtained by summing all contributions of the universe

u is speed of m2 relative m1

(from Hubbles law)

-grav

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Summary

• Weber Force verified by Liverpool Experiment

• Weber Force explains Meissner Effect

• Weber Force indicates Origin ofInertial Mass (Einstein 1950)