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Practical Applications ofWeber Force
byKjell Prytz
University of MalardalenVasteras, [email protected]
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)