How to Convert an Einstein Special Relativity (ESR) Equation into a
Corresponding Absolute-space Equation
The “Key” is a simple equation. It converts an Einstein abstract-space
equation into a corresponding absolute-space equation. Its derivation is
detailed in DSSU Relativity --The Lorentz
Transformations Applied to Aether-Space, Physics Essays Vol 23,
No.3 (2010 Sept). In that Paper the Key appears as equation (4-7):
.
(4-7)
The symbols
u,
uA, and
uB represent
collinear velocities or velocity components; c is the speed of
light. The absolute motion of reference frame “A” is given by
uA, and the
absolute motion of reference frame “B” is given by
uB. And the
relative motion between them is u.
This equation serves three purposes:
(i) converts the absolute speeds
uA and
uB to a
relative speed; (ii) ensures the predicted observable relative speed
u is always less than
c; (iii) links any Einstein special relativity (ESR)
expression to the (DSSU) Absolute equivalent equation. |
The Apparent-to-Absolute
Transformation Equation Anyone familiar with relativity will notice a certain
similarity with the ESR Addition of Velocities equation. However,
the similarity is superficial.
Let me clarify that I am not taking one of Einstein’s
relativity equations and presumptuously applying my own label. My
equation is actually derived from an aether theory and achieves the
conversion by using the absolute motion of two reference frames. The
Einstein velocity transformation
equation (shown in Flowchart 4 below, and also known as the
Relativistic Law of Addition of Velocities) achieves the conversion by using the
relative motion of the reference frames. In both cases the
purpose of the transformation is to extract an apparent relative
speed/velocity.
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Our interest is focused on purpose (iii).
To make the conversion from an Einstein abstract-space equation to an
absolute-space equation we simply substitute the above expression and do the
algebra.
First we’ll convert the commonly used Lorentz factor.
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Flowchart 1.
Lorentz factor (gamma, g)
conversions.
To go from ESR to DSSU the procedure is to substitute the conversion
equation. To go from DSSU to ESR the procedure is as follows: Observer
in frame A considers himself motionless, thus
uA is
replaced by zero. Then the motion of frame B becomes the
relative motion; and so
uB
is replaced by
u.
Note that gA
is the ‘absolute’ Lorentz factor (1− (uA /c)2)−1/2;
and gB
is the ‘absolute’ Lorentz factor (1− (uB /c)2)−1/2. |
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When converting the aether-referenced Lorentz factors,
gA and
gB, use the same method
stated in the caption for Flowchart 1. Change
the velocities from ‘absolute’ to ‘apparent’ (or relative). That is, change the
velocities for A and B from aether-referenced to
observer-referenced.
Time Dilation
Consider an observer in frame A and another observer in frame B.
The two frames are in relative motion with respect to each other. And,
they are also in absolute motion with respect to aether-space. Next,
consider the time interval between two events —such as two ticks of a clock.
Dt0
is a clock-time interval measured within, say, frame B; while
Dt
is the corresponding time interval determined by the observer in frame A.
The question is, “How does observer B’s
Dt0
compare with observer A’s clock-time?”
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Flowchart 2.
Time dilation equation conversions. To go from ESR to DSSU
the procedure is to substitute the conversion equation. To go from DSSU
to ESR the procedure is as follows: Observer A considers himself
motionless, thus
uA is
replaced by zero. Then the motion of frame B becomes the
relative motion; and so
uB
is replaced by
u.
Dt0
is the proper time measured in, say, frame B. |
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Observer A “sees” that observer B’s time as being dilated. In
other words the relatively moving clock appears to run slower.
Note that the gamma factor (g) is
always greater than unity. However, the difference between
g and 1 is not significant unless the
velocity is greater than one-tenth the speed of light.
Length contraction
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Flowchart 3.
Length contraction equation conversions. To go from ESR to DSSU the
procedure is to substitute the conversion equation. To go from DSSU to ESR the procedure is as follows: Observer A considers himself
motionless, thus
uA is
replaced by zero. Then the motion of frame B becomes the
relative motion; and so
uB
is replaced by
u.
The conversion also applies to the various gamma (g)
factors as detailed for Flowchart 1. |
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Velocity transformation
The velocity transformation equation, shown in
Flowchart 4, is also known as the relativistic law of addition of
velocities. It transforms an apparent velocity u′ within one frame,
say B, into an apparent velocity u for an observer in the other
frame (relatively moving frame).
Simply put, if an observer B measures the speed of some object to be
u′ then observer A will find the speed of the same object to be
u.
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Flowchart 4.
Velocity transformation equation conversions. To go from ESR to
DSSU the procedure is to substitute the conversion equation. To go from
DSSU to ESR the procedure is as follows: Observer A considers
himself motionless, thus
uA is
replaced by zero. Then the motion of frame B becomes the
relative motion; and so
uB
is replaced by
u. |
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What is significant about the DSSU expression is that the transformation of
an apparent velocity/speed (apparent speed u′ into apparent speed
u) is accomplished by the use of absolute motions.
Relativistic linear momentum
The momentum of an object is defined as the product of its mass times its
velocity. The classical expression, suitable for normal speeds, is,
p = m
u .
When the velocity magnitude is a significant fraction of the speed of light,
rest mass m must be replaced by the relativistic mass, expressed
as g mo.
The expression for relativistic mass is a mathematical consequence of
the Lorentz transformation and the law of conservation of momentum.
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Flowchart 5.
Relativistic linear momentum equation conversions. To go from ESR
to DSSU the procedure is to substitute the conversion equation. To go
from DSSU to ESR the procedure is as follows: Observer A
considers himself motionless, thus
uA is
replaced by zero. Then the motion of frame B becomes the
relative motion; and so
uB
is replaced by
u.
(The g
factors are handled as previously detailed for
Flowchart 1.) |
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Relativistic Kinetic Energy
The relativistic kinetic energy of a particle (or mass) is defined as
the difference between the total energy, and the rest energy.
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Flowchart 6.
Relativistic kinetic energy equation conversions. To go from ESR to
DSSU the procedure is to substitute the conversion equation. To go from DSSU to ESR the procedure is as follows: Observer A considers
himself motionless, thus
uA is
replaced by zero. Then the motion of frame B becomes the
relative motion; and so
uB
is replaced by
u.
(The g
factors are, again, handled as detailed earlier.) |
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The Detection of Absolute Motion —Reality and Method
Absolute motion was first detected in the year 1887 by Albert Michelson and
Edward Morley. This “absolute motion” was, of course, with respect to the aether
that pervades the universe and fills all space.
There are two practical methods for measuring absolute motion (its magnitude
and direction). One is the traditional method (based on a 2nd order
effect of
u/c); the other is a
comparatively new method (based on a 1st order effect of
u/c). The first method is the
gas-mode Michelson optical interferometer and dates back to 1887. It is a
cumbersome method that measures an extremely weak effect (an effect that has
often been misinterpreted). The second method involves the RF light-speed
anisotropy detector. It was developed, in 2006, by Professor Reginald T.
Cahill of Flinders University in Australia. His method involves timing the
difference between a radio-frequency signal and a fiber-optic light signal along
a common path length and recording the anisotropy that occurs as the Earth and
laboratory rotate with respect to the celestial sphere.
For the details on this 1st -order method of
measuring absolute motion (magnitude and direction) see Cahill’s remarkable
research paper, A New Light-Speed Anisotropy Experiment: Absolute Motion and
Gravitational Waves Detected (Progress in Physics, October, 2006 Vol.
4) p73-p92 [Posted at:
http://www.mountainman.com.au/process_physics/HPS33.pdf ]
What About the Cosmic Absolute Reference Frame?
What about the well-known absolute frame of reference provided by the CBR
—the frame in which the CBR is isotropic)? ... This frame is highly useful for
referencing cosmic scale motions, such as the drift of galaxies and other
astronomical objects —and even the flow of aether-space itself ! But it has no
practical use in special relativity. The reason is that relativity
(whether ESR or DSSU) applies to ‘local’ motions only. It applies to local
motion only, because Relativity Theory is dependent on what local aether-space
is doing (how it is moving) —in Einstein’s version, of course, it depends on
what local abstract-space is doing (how it is curving/distorting).
How Important is Absolute Motion?
It turns out that absolute motion is the very cause of relativistic effects
—both apparent and intrinsic. Absolute motion is what determines
observer-dependent effects as well as observer-independent effects.
Most importantly absolute motion is now understood to be the cause of the
various relativistic effects, in complete contradiction with the Einstein
viewpoint, but in accord with the earlier proposal by Lorentz.
—Reginald T. Cahill [The Speed of Light and the Einstein Legacy:
1905-2005 Published in: Infinite Energy, Volume 10, Issue 60
(2005) pp. 28-37]
(This Part-2 article has focused mainly on the apparent effects
—the ones that depend on the apparent relative motion between two
frames, two observers. The absolute effects are detailed in the full-version
Paper.)
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Copyright © 2010
by Conrad Ranzan E-mail:
Ranzan@CellularUniverse.org
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