Murat

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RATES OF CHARGED CLOCKSIN AN ELECTRIC FIELD

• Murat Özer
• Greenbelt, MD
• murat.h.ozer_at_gmail.com

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• This is not an Alternative Gravity talk.
• PURPOSE
• 1) Present arguments for the electrical effects
  of
• i) Time Dilation
• ii) Redshift
• iii) Spacetime Curvature
• (Currently these effects are believed to not
  exist independently of Gravity)
• 2) Show that the Special Relativistic
  
• Electromagnetism is an approximation to an
• exact General Relativistic Multi-Metric
  Theory
• 3) Present the implications of this resulting
  theory

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• The Gravitational Arguments for the Time
  Dilation ,
• Redshift Spacetime Curvature will be
  adapted
• to Static Electric Fields.
• Argument 1 Consider two identical atoms at
  different
• potentials in a Gravitational Field two
  identical
• charged atoms (ions) at different potentials in
  an
• Electric Field separated by a distance H.
• 
  

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• When the atom at the origin is in an excited
  state
• with an excitation energy E0 its total
  energy is

Gravity
Electricity

• When the photon emitted by this atom is
  absorbed
• by the atom at position H, its energy
  becomes

• The fractional difference in the atomic energy
• levels of the two atoms is

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• The energy levels of the absorber atom are
  blueshifted (irrespective of Q) in Gravity, and
  for positive Q in Electricity in the laboratory
  frame
• Eq. (1) describes the difference in the rates of
  atomic clocks located at a height H one above the
  other.
• (For Gravity L. B. Okun, K. G. Selivanov,
  Am. J.Phys. 68 (2000)115 )

A positively charged atomic clock runs faster at
points of higher electric potential than
at points of lower electric potential.
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• The photon emitted by the absorber atom will
• appear to undergo a Redshift for positively
• charged atoms

It is essential to note that the photon is
electrically neutral or that it has no
effective electric charge has nothing to do
with the Electrical Redshift.
We propose a Pound-Rebka-Snider experiment in an
electric field with ions to verify Eq. (2).
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• Argument 2 Pendulum Clocks suffice to detect
  the
• existence of the Time Dilation both in Gravity
  Electricity
• Let us treat the Gravitational Case First
• Consider two identical simple pendulums of
  length
• L located vertically at z0 and zH.
  The periods
• of the lower and upper pendulums are given
  by

Gravitational Time Dilation (with a
wrong magnitude)
then
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• Let us adapt the gravitational case to
  electricity
• Consider a Charged Simple Pendulum above a
• charged sphere. The period of the pendulum
  is

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Predicted times elapsed after 105 oscillations
of a charged simple pendulum with L25 cm, m100
g, r1cm, in the downward electric field produced
by a metallic sphere of R12.5 cm, V(R) -105 V.
A positively charged pendulum (clock) runs
faster at points of higher electric potential
than at points of lower electric potential.
This is the Electrical Time Dilation
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• Use the last part of Schilds Argument
• Two Photons are emitted by the charged clock at
  z0
• which are absorbed by the charged clock at
  zd in an
• electric field. The emission absorption
  time intervals
• are not equal.
• A parallelogram with unequal opposite sides
  cannot be
• realized in Minkowski Spacetime.
• Spacetime must be curved in the presence of an
• electric field.

Charged pendulum clocks provide an experimental
proof for the Electrical Time Dilation
Spacetime Curvature
A Pound-Rebka-Snider Experiment must be done, too.
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Argument 3 Adapt Torrettis Gravitational
Argument (R. Torretti, Phys. Perspect. 2 (2000)
118)

• Consider a charge distribution concentrated at
  a point. The electrical field around such a
  charge distribution is nonuniform.
• Move from one field line to the other and come
  back to the
• original point by making a 3600 rotation.
• Cover all the field lines in 3 dimensions.
• The set of points obtained this way constitute
  the two
• dimensional closed surface S2.

Differential Topology The set of all rays
emanating from a point is a representation of the
manifold S2. (Gravitation, Misner, Thorne,
WheelerSec. 9.7)
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• Argument 4 The Electrical Redshift/Time
  Dilation can be
• Inferred from a Principle of Equivalence (PE)
  for the Electric Field.
• Note that The Gravitational PE has been stated in
• different forms some of which are extraneous
  and wrong.
• The statement There is no local experiment that
  can
• distinguish a uniform gravitational field from
  a uniform
• acceleration is
• extraneous in that it is not required for the
  equivalence
• of uniform acceleration and gravitational
  field at a point,
• incorrect. (An electron in uniform acceleration
  radiates while it
• does not when it is at rest or moving at
  constant velocity in a uniform gravitational
  field S. Parrot, Found. Phys. 32 (2002) 407)

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• We adapt R. C. Tolmans definition
  (Thermodynamics and
• Cosmology, Dover Publications, Inc. 1987) to
  electric fields
• Replace gravity by electricity in the definition
• It is always possible at any spacetime point of
  interest
• to transform to coordinates such that the
  effects of
• electricity will disappear over a differential
  region in the neighborhood of that point, which
  is taken small enough so that the spatial and
  temporal variation of electricity within the
  region may be neglected.
• The equation of motion for a charged particle
  moving
• freely in an electric field E is

mi inertial mass, q electric charge
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• The transformation

transforms Eq.(3) to

• Hence, the electric field in the vicinity of
  the particle
• has been cancelled.

• Uniform acceleration is equivalent to charge
  to mass
• ratio times the electric field.
• The resulting General Relativistic theory will
  be a
• Multi-Metric theory.
• Now consider a cabin or a spaceship uniformly
• accelerating at
  in a region devoid of
• any kind of fields.

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• A photon emitted at t0 by an emitter is
  absorbed by a
• receiver at position H at tH/c. The absorber
  is receding
• at velocity
  and detects
• the photon at the Doppler shifted frequency

• The fractional change in frequency is the same
  as that
• in Eq. (2).

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• Conclusions Implications
• For a spherical object of mass M and charge Q,
  the
• metric outside it in the presence of a test
  particle of
• mass m and charge q is given by

• The Special Relativistic Electromagnetism
  based on
• the flat metric is an approximate theory in
  the presence
• of nonuniform electric fields.
• The exact theory is a General Relativistic
  (Geometric)
• multi-metric theory based on the above metric.

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• is NOT the Gravitational Field
  (because of the
• electrical contribution to ds2 its just
  the metric
• tensor).
• The present Quantum Gravity is NOT Quantum
• Gravity. It is Quantum Spacetime Geometry.
• Objects that can be called Black Holes for
  Electrons
• or other charged objects can be built in the
  laboratory.

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• The rate of development of science is not the
  rate at which you make observations alone but,
  much more important, the rate at which you create
  new things to test.
• Richard Feynman