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1.
Introduction.
The exact
position where a star appears in the sky does not only depends on the
coordinates
of the source observed, but also on the observer's relative
velocity. The
observer velocity is responsible for a phenomenon called "Bradley
aberration"
or "Stellar aberration". Stellar aberration is a well known
phenomenon
among astronomers. It was discovered by the astronomer James
Bradley [1]
in 1727. It is claimed to be caused by the relative transverse
motion
between
the earth and the star emitting the photons.
Some authors
[2-5]
have shown that this prediction is not fully compatible with
observations. There is no available explanation for the fact
that, while the
observational
data on stellar aberration are compatible with a moving earth, the
symmetric
description, when the star (and not the observer) possesses the
relative
transverse motion, does not apparently lead to observations compatible
with predictions.
2.
Radial
Velocities.
Each
component
of relative motion between a source and a detector is discussed here
separately. In the case of radial motion, it is well known that
the relative motion
between the source and the detector produces a change in wavelengths,
explained
by the "Doppler effect". There is then no change of direction of
the
photons. The radial velocity is compatible with the difference of
radial
velocities
between the star and the detector. According to Einstein's
relativity,
the condition of invariance implies that there exists no absolute
velocity
of the source or of the detector. Observations have shown that in
the
case
of radial motion, data are in full agreement with Einstein's
predictions.
3.
Transverse
Velocities.
In the case
of transverse motion between the two objects, another effect called
"Aberration
of Light" is predicted and observed. Following Einstein's
relativity, a
symmetrical situation is expected whether the source or the detector
possesses
the transverse velocity. Just as with the Doppler effect, the
Einstein's
principle of relativity also means that only the relative motion is
relevant.
However, it
has been demonstrated [2-5]
that some observations
are not compatible with those predictions. The seriousness of the
problem
has even been overlooked. Of course, the absence of a suitable
explanation
leaves the phenomenon of aberration of light without any rational
solution. It has been claimed that the observed results, which
depend on whether
the earth or the star is moving, are experimental proofs of the failure
of Einstein's principle. Let us examine that problem.
4.
Description
of the phenomenon.
One knows
that the earth completes a full circumference around the Sun every
year. Consequently, since the Earth-Sun radius (Re) is
well known,
it is easy to determine the earth tangential velocity (Vt)
required
to complete the circumference in twelve months (T seconds). We
have:
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We read in astronomy textbooks, that the relative velocity between photons (at velocity c) and the Earth (Vt), explains why a telescope "T" on Earth (see Fig. 1) must be pointing at the angle q , with respect to the Earth-star direction, to be able to point out at the star. Figure 1 shows that while the photons move in straight line toward the Earth, they will always remain in the axis of an inclined telescope, since it is moving sideways with the Earth. The angle q is equal to:
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5.
Apparent
Lack of Symmetry.
A serious
problem is revealed when one reads the description of that
phenomenon. Scientific papers and textbooks on relativity [6]
state or imply that stellar aberration is determined by the "relative
velocity"
between the light source and the detector. It has been clearly
shown
experimentally
that it is not so. Many convincing arguments have been pointed
out by
H.
Ives [2], Eisner [3],
and
Phipps
[4], and
Hayden [5],
and several others to show that when the source (instead of the
detector)
is moving, the aberration no longer exists. Observations show
clearly
that,
in contradiction with special relativity, stellar aberration does not
depend
on the relative motion between the source and the detector but exists
only
when the detector is moving. Textbooks explain the results solely
when
the observer is moving. There is no known explanation for the
case when
the source is moving.
That lack
of symmetry, between the cases whether the source or the detector is
moving
is shown clearly [5]
on the basis of the
separation of binary stars. One can reliably determine the motion
of
individual
stars of a binary system from their spectrum from the periodic Doppler
shifting of the spectral lines of the star components. Therefore,
stars
of a binary system acquire sufficient relative transverse velocity to
produce
an important aberration. Such an aberration is not
observed. Some
papers
report non realistic hypotheses to explain aberration when the star is
moving. The explanation goes from the claim that we do not
observe
reality
or the "Umbrella Analogy" mentioned by Eddington and some others.
6.
Mechanism
of Aberration.
Let us
consider
on figure 2, a stellar source S and a detector located on Earth.
Source
S emits photons in all directions at velocity c. In physics,
photons
are
conceived as being particles and are represented as bullets ejected
from
the surface of the emitter S with a velocity c. After a short
interval
of time after emission, the photons emitted at one instant form a
sphere
around the star as shown (dotted circle) on figure 2. Let us
consider
now
that the star S (instead of the Earth) has a transverse upward velocity
as shown in figure 2.
We know that the resulting velocity U of the emitted bullets (photons) is the relativistic sum of the star velocity V and the speed of light c. From figure 2, we see that V is perpendicular to the direction of light going to earth. The general velocity composition formula giving the sum of V and c, as given by Møller [6] is:
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7.
Compatibility
with Einstein's Theory?
This result
must be examined in terms of relative motion. It is stated in
relativity
that there exists no absolute velocity. Only the relative
velocity
between
two objects has a physical meaning. How can this be compatible
with the
above description of stellar aberration? This apparent paradox is
solved
when one considers more carefully what those two objects are. In
the
case
described above, the aberration of light clearly involves the relative
motion between the bullets (photons) and the detector. It does
not
involve
the relative motion of the system that has fired the bullets (called
source). In fact the star, from which the particles are emitted
is no more than
the support from which the particle (bullets) originated.
Erroneously,
the relative velocity between the star and the earth has been
considered
while one should consider the relative velocity between the incoming
particles
(bullets or photons) and the earth. Using that last consideration
we
find
at last that the principle of relative motion described by Einstein can
be applied in this case.
The error
of interpretation discussed here is exactly similar to the situation
that
appears when a hunter is firing at his prey. Nobody ever claimed
to be
able to calculate the transverse velocity of a running hunter from the
knowledge of the direction of the bullet moving toward the prey.
The
angle
of penetration of the bullet into the prey depends on the relative
velocity
between the prey and the bullet and not the velocity relative to the
hunter. If the hunter is running forward, he must point his gun
with an angle
having
a backward component to reach his target.
One must
conclude
that it was an error to claim that the aberration of light is caused by
the relative transverse velocity between the star and the Earth.
One
should
say that it is the result of the relative transverse velocity between
the
Earth and the coming photons. Consequently, in this particular
case,
Einstein's
principle of relativity can be applied.
8.
Case
for Other Models for Light.
It can be
seen quite easily that the explanation given above about the aberration
of light can be applied to the wave model of light just as well as to
the
model of photons. The consequences are quite identical. No
aberration
of
light is expected when the emitter (instead of the wave) has a
transverse
velocity. One can also ask the question: "Can we find a similar
interpretation
for the aberration when light is described according to modern physics?
One must recall that modern physics finds its interpretation with the
use
of the Copenhagen interpretation. The Copenhagen interpretation
implies
that photons cannot exist independently of the observer and are created
at the moment of detection. Consequently, the explanations given
here
cannot
be applied directly. In fact the question does not make sense
since in
modern physics, it is claimed that explanations do not necessarily have
to be compatible with causality. This is stated clearly by
Heisenberg
himself
when he writes: "The law of causality is no longer applied in quantum
theory". When we do not accept the principle of causality it does
not make sense
to look for the cause of stellar aberration.
However,
without
changing the mathematics of modern physics, (but without using the
Copenhagen
Interpretation of Modern Physics), it is possible to show that physical
phenomena can be described in a causal way. This has been shown
in more
details recently. It can be shown that, using a causal
description of
modern
physics, the phenomenon of stellar aberration of light" is explained
classically.
Acknowledgment.
The author
wishes to acknowledge the financial assistance of the National Science
and Engineering Research Council of Canada, and exchange of
correspondence
with Dr. T. E. Phipps.
==================
[1] J. Bradley "Account
of
a New Discovered Motion of the Fixed Stars" Phil. Trans. 35 p. 637
(1728).
[2] H. E. Yves "Extrapolation
from
the
Michelson-Morley
Experiment" J. Opt. Soc. Am. 40, pp.
185-190
(1950)
Also - P. Marmet, “The
Overlooked
Phenomena
in
the
Michelson-Morley
Experiment”
[3] E. Eisner, "Aberration
of Light from Binary Stars - a Paradox?" Am. J. Phys. 35,
pp.817-819
(1967)
[4] T. E. Phipps "Relativity
and Aberration," Am. J. Phys., 57, pp., 549-550 (1989) also Phipps
T. E., Jr., "Stellar Aberration from the standpoint of the Radiation
Convection Hypothesis." Phys. Essays
4,
368, (1991)
[5] H. C. Hayden, Stellar
Aberration," Galilean Electrodynamics, 4. pp. 89-92 (1993)
[6] C. Moller, The Theory
of Relativity, (Oxford 1972)
[7] W. Heisenberg, "Physics
and Philosophy, the Revolution in Modern Science" New York, Harper
and Row, (1966) p. 88
[8] P. Marmet, "Absurdities
in Modern Physics: A Solution" Les Éditions du Nordir,
Simard
Hall, 165 Waller, Ottawa, K1N 6N5, Canada (1993).