The recently reported time dilation effect in Type Ia supernova SN 1995K has been claimed to rule out the static universe model of Narlikar &amp; Arp. It is shown here that the variable mass hypothesis which accounts for the redshift phenomenon in the above static universe model does indeed predict the observed effect and that there is no conflict between the data of Leibundgut et al. and the predictions of this model

Arp, H. C.

Narlikar, J. V.

English

Publications of the IAS Fellows

TIME DILATION IN THE SUPERNOVA LIGHT CURVE AND THE VARIABLE MASS HYPOTHESIS
J. V. NARLIKAR1 AND H. C. ARP2
Received 1996 October 11; accepted 1997 April 2
ABSTRACT
The recently reported time dilation effect in Type Ia supernova SN 1995K has been claimed to rule out the
static universe model of Narlikar & Arp. It is shown here that the variable mass hypothesis which accounts for
the redshift phenomenon in the above static universe model does indeed predict the observed effect and that
there is no conflict between the data of Leibundgut et al. and the predictions of this model.
Subject headings: cosmology: observations— galaxies: distances and redshifts — supernovae: general —
supernovae: individual (SN 1995K)
1. INTRODUCTION
Leibundgut et al. (1996) have recently reported that in the
light curve of a distant Type Ia supernova, the rise and fall of
the light intensity is over a longer time span than similar events
in nearby supernovae. The supernova SN 1995K examined by
them exhibits a spectroscopic redshift of 0.479, thus suggesting
that it is present in a spiral galaxy of that redshift. In the
expanding universe hypothesis, this time dilation is explained
as the apparent increase in the observed timescales of an
object of cosmological redshift z by the factor (1 1 z). These
authors remark: “In a static universe, time dilation is not
expected to act on the light curve. Redshift in this case is
caused by tired light or an equivalent theory (e.g., the variable
mass hypothesis . . . ).” We show here that this statement is not
correct so far as the variable mass hypothesis is concerned. In
fact, we will demonstrate that the Narlikar-Arp model makes
the same prediction as the expanding universe model. In the
end, we will stress those observations that would indeed
distinguish between the two models.
2. THE VARIABLE MASS HYPOTHESIS
We begin with a summary of the theoretical basis of the
model discussed by Narlikar & Arp (1993, hereafter Paper I).
The gravitational theory underlying the model is conformally
invariant and incorporates Mach’s principle in the following
way. The inertial mass of a typical particle is determined by the
scalar field contributions from the rest of the particles in the
universe. The scalar interaction is conformally invariant in the
sense that if the measured inertia of a particle in a given
spacetime metric gik is m, then in a conformal transform V2gik
of this metric the mass will be m /V. For detailed mathematics
of this theory see Paper I and the references cited therein.
The resulting gravitational theory is wider in scope than
general relativity and is conformally invariant. One can also
show that, within this framework, the standard physics on
which all astronomical observations are based is also confor-
mally invariant at both the classical and the quantum level.
The outcome of this formulation is that one can look at the
standard expanding universe models in a different conformal
frame and still expect to see the same physical phenomena. Since
the Robertson-Walker models used in standard cosmology are
conformally flat, one can use a flat spacetime model to
describe the same cosmology. Thus one can use a static
Minkowski spacetime to describe the same phenomena com-
monly associated with the expanding universe. The difference
is that, whereas in the expanding model the particle masses are
constant, in the static model they increase with epoch.
How does the redshift arise in this cosmology? As explained
in Paper I, it cannot arise as the result of passage of light
through spacetime as it does in the expanding universe.
Instead it arises because the particle masses were smaller at
the source than they are at the receiver, since the source is
being observed at an earlier epoch. Atomic physics then tells
us that the wavelengths of standard spectral lines, being
reciprocal to the masses, were longer at the source than at the
receiver. Hence the redshift is given by
1 1 z 5
mreceiver
msource
. (1)
The redshift-magnitude relation in this cosmology therefore
depends not on any expansion factor but on how the way the
inertial mass depends on the epoch t. The simplest solution
described in Paper I had
m~t! 5 t2 . (2)
It was shown there that the transformation of this model to
the conformal frame in which particle masses are epoch
independent leads to the standard k 5 1 Friedmann model,
also commonly known as the Einstein–de Sitter model. The
epoch t 5 0, when the particle masses all vanished in the static
model, corresponds in standard cosmology to the singular
beginning of the universe.
Thus this cosmology is observationally indistinguishable
from the standard Friedmann cosmology if one sticks to tests
like Hubble’s law, source counts, angular size–redshift rela-
tion, surface brightness test, etc. The supernova light-curve
test also falls in this class, as we shall now see.
3. APPLICATION TO SUPERNOVA PHYSICS
We now consider the observations of supernovae at large
redshifts. In the static model with the variable mass hypothesis,
a supernova at redshift z . 0 will be made of particles of
masses lower than those in a currently observed local super-
nova, by a factor (1 1 z)21. This mass difference applies to all
subatomic particles and therefore all dynamical and atomic
timescales will be scaled up by this factor. It is generally
accepted that the light curves of Type I supernovae result from
1 Inter-University Centre for Astronomy and Astrophysics, Post Bag 4,
Ganeshkhind, Pune 411 007, India.
2 Max-Planck-Institut fu‹r Astrophysik, 85740 Garching, Germany.
THE ASTROPHYSICAL JOURNAL, 482 :L119–L120, 1997 June 20
q 1997. The American Astronomical Society. All rights reserved. Printed in U.S.A.
L119
the formation of 56Ni, which decays to 56Co and then into 56Fe.
Since these decay times run on the slower clock times of lower
mass atoms, they are time dilated by exactly the (1 1 z) factor
derived either from the more general Narlikar-Arp or the
special case Friedmann solution for the general relativistic
field equations.
Any differences in the radiation transfer in the expanding
gas of lower mass particles would lead to, in first order,
zero-point delays. Remaining differences would be masked in
the variation of decay rates which is observed in Type I
supernovae. For example, there have been factors of 3–5 in
energy and considerably different decay rates observed. (Tu-
ratto et al. 1996; see also Goldhaber et al. 1997).
This is the reason why we expect the timescale associated
with the light curve to be scaled up by this factor. Hence the
result observed by Leibundgut et al. (1996) is fully consistent
with this model, as it is with any expanding universe model.
The interpretation of time dilation is different in the two cases.
In the standard cosmology this is due to the expansion of
space, whereas in the static model it is due to the slower
timescales associated with smaller masses of younger particles.
4. CONCLUDING REMARKS
The difference between the two models comes into focus
when one is describing anomalous redshifts. The essential new
feature in this cosmology that distinguishes it from the stan-
dard one is the possibility that in it new matter may be created
in explosive events at t 5 t1 . 0. The new matter would have
zero particle masses at this later epoch t1, and these masses
would subsequently grow as (t 2 t1)2. Such matter will there-
fore be made of particles with masses systematically lower than
particles which had their zero-mass epoch at t 5 0. Thus a
quasar ejected from a galaxy and remaining in its neighbor-
hood will have a redshift higher than that of the parent galaxy.
This theory therefore provides a natural explanation for the
phenomena of anomalous redshifts, without in any way con-
flicting with the standard phenomena associated with the
expanding universe models. We will not go into details of this
aspect, which has already been highlighted in Paper I.
One could, however, ask whether matter ejected in super-
novae has also been created very recently and therefore carries
anomalous redshifts. If this were the case, supernova-related
redshifts would not show a tight Hubble relation. The evidence
at low redshifts does show a good Hubble relation, and
accordingly the supernova matter does not carry anomalous
redshifts. The origin of this matter therefore dates back to
t 5 0, and the explanation given in § 3 will apply. Supernova
studies at high redshifts will be of interest in setting limits on
the anomalous redshift component.
REFERENCES
Goldhaber, G., Deustra, S., & Gabi, D. in Thermonuclear Supernovae, ed. P.
Ruiz-Lapuente, R. Canal, & J. Isern (Dordrecht: Kluwer), 777
Leibundgut, B., et al. 1996, ApJ, 406, L21
Narlikar, J. V., & Arp, H. 1993, ApJ, 405, 51 (Paper I)
Turatto, M., Bennetti, S., Cappelaro, E., Danziger, I. J., Della Valle, M.,
Gouiffes, C., Mazzali, P. A., & Patat, F. 1996, MNRAS, 283, 1
L120 NARLIKAR & ARP


Time dilation in the supernova light curve and the variable mass hypothesis

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Time dilation in the supernova light curve and the variable mass hypothesis

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