symposium talk on origin of magnetic and strong force in relativistic kinematics, david c lush

7/27/2019 Symposium Talk on Origin of Magnetic and Strong Force in Relativistic Kinematics, David C Lush

http://slidepdf.com/reader/full/symposium-talk-on-origin-of-magnetic-and-strong-force-in-relativistic-kinematics 1/40

The Magnetic Force as a

Kinematical Consequence of theThomas Precession

David C. Lush

Presented at PIERS 2013 Stockholm

14 August 2013

[email protected]

quantumskeptic.blogspot.com



Work in Progress

• The following describes a work in progress,

so is subject to revision

• As updates become available they will be

posted as replacements at arxiv.org.

(Search author: Lush, same title as for

PIERS talk and paper)



Why a kinematics point of view?

• Can start with a Coulomb force, in a

reference frame where the field-source

charge is stationary, and then get magnetic

force present in other reference frames,without reference to electromagnetic fields

• Predicts new forces?

• Unifying principle for non-gravitational

fundamental forces?



Field-Source and Test Charged Particles

(r,

t ) = (r

t -r

s,

t )

Lab frame

observer

Source particleTest particle

qt , mt

qs , ms

r t (t )

v t (t )

a t (t )

Test particle

position,

velocity and

acceleration

r s (t )

v s (t )

a s (t ) = 0

Source particle

position and

velocity

= Charge, mass



Magnetic force between two charges

The magnetic force is formally

similar to a Coriolis force



Rotational pseudoforces review

“Effective” force in a coordinate system rotating with

angular velocity w is the force applied in the non-rotating

system, plus Coriolis, centrifugal, and Euler pseudoforces.

Coriolis centrifugal Euler



Thomas precession

• Translating and cross-accelerating reference

frame appears to rotate

• A consequence of noncommutativity of

non-colinear Lorentz boosts

• Invoked by Thomas to explain spin-orbit

coupling anomaly

• Observer dependent

• Has to be observed mutually between two

observers if seen by either



Angular Velocity of the Thomas

Precession

Angular velocity of the rest frame of a particle with

acceleration a and velocity v in the laboratory

frame, as observed from the laboratory frame.

(Jackson, Classical Electrodynamics, 2nd ed, Eq.

(11.119))

for v/c << 1



Thomas precession cannot

generate rotational pseudoforces

• An accelerating observer sees Thomas

precession of inertial coordinate frames

– Will present proof – The accelerated observer sees a lack of

pseudoforces as having dynamical effects (i.e.,

real forces acting)



Sign of the Angular Velocity of Thomas Precession,

as Seen by Different Observers

Jackson Eq. (11.107) :

, with

More generally:

So if (as seen from lab frame):

Then (as seen from rest frame):

The sign of the angular

velocity of the Thomas precession of the lab

frame is opposite that

of the rest frame. (See

also Malykin 2006.)

(see, e.g., Goldstein)



The Magnetic force as a Coriolis Force seen

by the Test Particle Co-Moving Observer

• The test particle co-moving observer (TPCMO) sees Thomas precession of both

the source particle and laboratory frames

• Since the TPCMO knows that the test particle acceleration is purely radial

(Coulombic) in the (inertial) source particle

rest frame, he expects a Coriolis-like forceto exist in the lab frame based on the

relative angular velocity of the lab frame

compared to the source frame



Relative Thomas Precession Angular Velocity of

Lab Frame Compared to Source Frame, as seen

by the Test Particle Co-Moving ObserverAngular velocity of Thomas precession

of an inertial frame, as seen from an

accelerated frame.

Lab frame angular velocity as seen from

test particle rest frame.

Source particle rest frame (SRF) angular

velocity as seen from test particle rest

frame.

Relative angular velocity of lab frame

compared to SRF as seen from test

particle rest frame.



The Magnetic Force as the Expected Coriolis

Force Due to Relative Angular Velocity

(per chart 7)

expected Coriolis force in lab frame

relative angular velocity of lab frame

compared to SRF as seen from test

particle rest frame (from previous chart).

The test particle acceleration is approximately Coulombic, obtaining

and had

Substituting for gives



Is the Magnetic Force a Coriolis or an Anti-

Coriolis Force?

• The above derivation characterizes the

magnetic force as a Coriolis force, but it is more

properly an anti-Coriolis force

• The magnetic force is ultimately a consequence

of the lack of Coriolis force in the source particle

rest frame (an inertial frame), despite its

appearance of rotation to the TPCMO



A More Rigorous Analysis of the Kinematics of

the Two-Body Electromagnetic Problem

• An exact relativistic-kinematic description of the two-body electromagnetic interaction is needed to check for

consistency of physical law with relativistic covariance

• Starting in the source particle rest frame where the

motion is easy to describe, obtain motion in lab frameby making a series of Lorentz transformations of the test

particle position, first to the test particle rest frame,

then to the lab frame

– The expected result is a description of the motion in the lab

frame, as predicted by the TPCMO

• Today will present an overview of first part

– Contend the results shows the necessity of anti-Euler and anti-centrifu al forces in addition to the anti-Coriolis force



Coordinate Systems for Derivation of Thomas Precession

(as Seen by Test-Particle Co-Moving Observer)

(r,t )

(r,t )

(s,x )

Source particle rest

frame (equivalent to

lab frame with a

stationary source

particle, for thisanalysis)

Test particle

momentary rest

frames

Test particle (t.p.) and

co-located, co-moving observer

t is the t.p. proper time,

r is the t.p. displacement

from the field-source

particle, as observed by

the observer co-moving

with the test particle

(s,x ) = (0,0) at (r,t)= ( 0,t 0)

(s’,x ’) = (0,0) at (r,t)= ( 0,t 0+ d t )

(s’,x ’)

= test particle

position in source

rest frame



Significance of the Accelerated Observer

• Same legitimacy as an inertial observer (the

principle of relativity)

• Must be able to describe physics in inertial

frames based on observations in his frame



Prior Work: Bergstrom

• Similarities: Accelerated observer, mass factor cancels

• Differences: "mosaic" avoids expectation of

centrifugal/Euler forces

• Mosaic argument disproved by sequential Lorentz

transformations of displacement?

• Also notable: observes effect applies to gravity too;

implies gravitomagnetism



Counter-argument to Bergstrom’s claim of

impossibility of centrifugal effects of Thomas

precession

• Sequential Lorentz transformations of

displacement should obtain directly anti-

Euler and anti-Centrifugal forces (work still

in progress)

• Both have explicit dependence on inter-

particle displacement

• Have preliminary result for test particle rest

frame: have obtained anti-Euler force



Velocity of Test Particle Relative to Source Particle as Seen by

Observer Co-Moving and Co-Located with the Test Particle

(see Moller, Theory of

Relativity, 1952 edition,

Eq. (146), page 257)(or

3rd chart following)

where

test particle velocity relative to source particle, as seen by TPCMO

and



Thomas precession of source rest frame as seen by TPCMO derived by

successive Lorentz transformations of displacement

Lorentz Transformation of

Test Particle Position from

Source Rest Frame to Test

Particle Momentary Rest

Frame at time t = t 0

Lorentz Transformation of Test Particle Position from

Source Rest Frame to Test

Particle Momentary Rest

Frame at time t = t 0 + dt



Variation of interparticle displacement as observed by

TPCMO with respect to time in source rest frame

where

Find that:

so



Time flow at the Field Source Particle as Seen by Test

Particle Co-Moving Observer

LT of time in TP momentary

rest frame to SRF:

Evaluate at location of

field source particle :

Then:

To order



Test Particle Velocity Relative to Source Particle as Seen From

Test Particle (Fermi-Walker) Rest Frame

where

Reduces to (to order b 2)

W

as expected



Relative Acceleration as Seen by Test Particle Co-

Moving Observer

Had

so

Apply chain rule as



Thomas Precession Angular Velocity Relations



Finding the Anti-Coriolis and Anti-Euler Accelerations in

the Test Particle Rest Frame Acceleration

Can’t find this term

Only have half of this

term

Anti-Euler terms are found

exactly



Finding the Anti-Coriolis and Anti-Euler

Accelerations in the TPRF Acceleration

(Expected anti-

Coriolis acceleration)

Based on relativistic law of inertia, need a Lorentz factor in derivative,

with respect to proper time, which obtains

Can re-write with anti-Coriolis force as



Finding the Anti-Coriolis and Anti-Euler

Accelerations in the TPRF Acceleration

Relative acceleration in

the test particle

momentary rest frame

Continuing effort is to interpret and refine this result, then

complete kinematic analysis to obtain description of motion

in laboratory frame.



Anti-centrifugal force

• Implication of lack of rotational

pseudoforces: a missing centrifugal force

predicts an always-attractive force (evenfor like charges)



Strength of Anti-centrifugal force

compared to Coulomb repulsion

(for b 1)

For circular motion (and neglecting delay):

Assuming equal masses and equating with relativistic Coulomb force, then

solving for R obtains :

for equal to the proton mass. This is about 100 times smaller than themeasured proton size.

Expect

Exact T.P. formula per Jackson:



Strong magnetic force

Exact magnetic force in Lienard-Wiechert magnetic

acceleration field:

Evaluate for particle 1 accelerated by Coulomb field of

particle 2 and assuming circular motion to obtain:

This magnetic force is always attractive, even for like charges.



Completeness of Lorentz force?

• Missing magnetic-like force?

– If the field-source particle is free to accelerate, then

expect an additional magnetic-like force, with mass

ratio factor

• Predicts an increase in strength of spin-orbit coupling in

hydrogen by factor (1 + 1836)/1836

• Unable to find basis in L-W acceleration fields

• Anti-Euler force? (Atomic scale dynamical

effects of terms at order v^2/c^2?)



Next steps

• Full relativistic kinematical proofs: order v^2/c^2 givesmagnetic, part of anti-Euler force

• Look for more T.P.-related forces in Maxwell-LorentzED

• Full relativistic kinematical proofs: order v^4/c^4 givesanti-centrifugal force, more of anti-Euler force

• Study time-symmetric dynamics of strong magnetic

force



Conclusion

• Relativistic-kinematical approach is a new

way to think about and describe

electromagnetic forces• Relativistic-kinematical approach may

reveal new electromagnetic forces

• Relativistic-kinematical approach ispossibly a new explanation for

fundamental forces



Backup/Extra



Submittal History

• Submitted to Physica Scripta Sept 2010

– Title: “Does Thomas Precession Cause

Rotational Pseudoforces in Particle Rest

Frames?” – Sent out for review, then review was cancelled

due to (my) statement that the submittal was

only a plausibility argument for the magnetic

force being caused by T.P.

• It is (still) only an order v^2/c^2 analysis



Pseudoforces of Rotation Do Not Occur

in Thomas Precessing Reference Frames

• For example, an accelerated observer sees

Thomas Precession of inertial frames

• See also UC Berkeley tutorial article by R. G.

Littlejohn linked in Wikipedia article on

Thomas precession: (page 8), ``... if we fix

ourselves to the parallel transported frame,we will feel no centrifugal forces.''



Schild

• Full relativistic ED description of two-particlecircular motion; time symmetric ED

• No negative relativistic mass bound state

(Sternglass mentioned)• No anti-centrifugal force found, but did not

invoke Coulomb acceleration; assumed onlycircular-centripetal acceleration

• Also, anti-centrifugal force wants to vanish undertime-symmetry



Problem 11.3 from Jackson

symposium talk on origin of magnetic and strong force in relativistic kinematics, david c lush

Documents